I don't think it changed much if anything in terms of terms of engagement. Supermarina imposed restrictive conditions on Campioni from day 1 (June 1940) and Taranto was not until November 1940. The Italians feared the British carriers - or carrier to be more precise - Eagle in east or Ark Royal in the west) and this led them to refuse combat even with the numerical - and firepower and speed - advantage.
I think you are making a confusion. There wasn't a time that Italians while "having advantage" retreated from combat because of a carrier. What Italians feared was night combat.
Btw the only time that carrier aircraft had success in fleet actions on Med was in Matapan, all others instances they failed to hit.
Try this in WITP-AE:
Level bombing successes of Regia Aeronautica against naval units at sea only - note the effect of near misses:
HMS Juno(sunk) Under high level bombing attack by five CANT Z1007 aircraft and hit by three bombs which split ship in two abaft the bridge structure sinking her in less than two minute. 116 of ship’s company lost their lives including one RAN rating, five locally Entered Maltese and a NAAFI Canteen employee.. 96 survivors were rescued, by HMS KINGSTON, HMS KANDAHAR and HMS
NUBIAN. Five of those rescued later died.
HMS Imperial(scuttled) near missed by level bombing of S.84
One of the bombs near-missed Imperial's stern, detonating in the vicinity of her propellers, with no immediately apparent consequences. Keeping station, Imperial arrived at Iraklion around 2030 hrs, embarked 300 troops and sailed for Alexandria at 0320 hrs, 29 May.
Shortly after 0345 hrs, while working up speed and already making 29 kn, the rudder, evidently damaged by the earlier near-miss, jammed, and the out-of-control destroyer cut across the bow of Orion, barely missing a catastrophic collision(from uboat.net). Was scuttled shortly after.
HMAS Nestor(scuttled)
Uboat.net: In the meantime, the 8 Cant.Z. 1007 bis attacked the convoy, at the time located some 100 nautical miles north of Tobruk, in position 33°36'N, 24°30'E. At 1806 hrs two bombs, dropped from 17000 feet (5000 metres) fell very close to Nestor's hull, causing a large hull breach in way of the engineering spaces abaft the stack, causing her to go dead in the water with severe engine damage and immediate flooding of #1 boiler room. All personnel in this section was killed, power failed and a fire broke out. It is only RAN ship that never saw Australia.
HMS Havok(damaged)- this was probably by S.81 based on Rodi(Rhodes)
During the Battle of Cape Spada on 19 July, the ship escorted the Australian light cruiser HMAS Sydney and rescued some of the 525 survivors from the Italian cruiser Bartolomeo Colleoni together with the other escorting destroyers. Her boiler room was flooded after an attack by Italian aircraft after this battle and she was repaired at Suez from 29 July to 15 September.
HMS Liverpool(damage):
From wiki seems to have been 2 hits:
Italian aircraft attacked Liverpool with bombs on 12 July(1940) while she was returning to Alexandria, Egypt, causing fatalities and wounding three, including the cruiser's commander.[34]
Later in July, Liverpool escorted convoy AN.2 from Egypt on its way to Greek ports in the Aegean and the southward-convoy AS.2 from the Aegean. The latter convoy came under substantial attack by Italian aircraft on the 29th; Liverpool was the only vessel hit when an unexploded bomb penetrated two decks,[35] killing a rating.
CVL HMS Eagle(damaged)Under heavy and sustained attacks whilst deployed with Fleet units in Aegean to provide aerial protection and anti-submarine patrols.Returned to Alexandria with Fleet units. Examination of hull revealed significant damage and accounted for contamination of aviation fuel system by damage caused during air attacks in recent weeks.Withdrawn from operational service and nominated for extensive refit.
HMS Gloucester(damaged)Wiki: The next day, a bomb dropped by Savoia-Marchetti SM.79 bombers struck the ship's bridge, killing 18 crew members instantly, including the captain.[11] As a result of the attack, the ship could not be steered from the bridge and was uncontrolled for a time before the aft steering position could take over. Despite an inoperable bridge, the ship remained with the fleet and participated in the Battle of Calabria on the 9th, although she was ordered away from the battleline to escort the aircraft carrier Eagle. It seems there were other hits afterwards with duds in other battles.
HMS Fortune:
(From wiki)During the return voyage on 10 May(1941), the ship was badly damaged by a 250-kilogram (550 lb) bomb that detonated nearby. The shockwave ruptured the hull, knocked out her engines, slightly bent her propeller shafts, and caused a lot of flooding. Her crew jettisoned nearly 18,000 pounds (8,200 kg) of topweight and she was able to reach a speed of 12 knots (22 km/h; 14 mph) en route to Gibraltar for temporary repairs. Fortune then sailed to Chatham Royal Dockyard for permanent repairs that lasted until November.[21]
HMS Firedrake:
(From wiki)During Operation Substance, Firedrake and Foxhound were each leading a column of the convoy, streaming their TSDS minesweeps, through the Sicilian Narrows on 23 July when an Italian 100-kilogram (220 lb) bomb near missed Firedrake and detonated off her port side. The shockwave blew in the plating over No. 1 boiler room and disabled her so that she had to be towed back to Gibraltar by the destroyer Eridge. Temporary repairs were made in Gibraltar and she was transferred to the Boston Navy Yard for repair on 23 September.