hmm, well first off, letting capitalships autocast as a rule is a bad idea(the AI sucks for most abilities). A few abilities are alright to autocast(perhaps Radiance Animosity, Rapture vertigo, and Halcyon Anima tempest are OK to autocast).
In general be wary of letting your ships autocast anything that will quickly run them out of AM. Even vertigo which I listed as "ok" can run Raptures out of AM quick at lower levels.
A few abilities to watch out for:
Vengeance on the Rapture sounds like a cool ability, but right now it sucks and is largely a waste of AM(so don't waste points in it).
Malice on the Progenitor is great when coupled with AoE damage, or extremely large amounts of weapons damage(if you have a colossal fleet), but most of the game if you lack AoE the AM would be better spent on Shield Regeneration. As a result Malice should never be left on autocast as the AI isn't smart enough to only use malice with AoEs. Also while malice may sound cool, it's generally the lowest priority skill on the progenitor to level up-Colonize is a huge boost to early game economy, and Regenerate shields is one of the single most important capitalship abilities the advent have.
As I'll touch on later the Radiance Battleship is a kind if weak capitalship, but if you do build it make sure to dump points in Detonate Antimatter first- it is by far the Radiance's best ability.
In general it sounds like you may be overusing Discipels a bit. Disciples are mostly only the body of your fleet early game. Late game Disciples are only really meant to counter support frigates and carriers. They get wrecked by heavy Cruisers and Long Range Frigates which are very common in late game fleets.
For fleet composition your main late game workhorses will generally be carriers loaded with bombers or Destra Crusaders rather then Disciples- these units should be where a bulk of your fleet's weapon damage comes from late game.
In particularly in the super late game carrier fleets are devastatingly powerful-together with the Rapture's Concentration Aura a fleet with maybe 50-60 squads of bombers is a mortal threat to any capitalship(and truly mature fleets with 80-100 squads can kill many capitalships from full in 2-3 bomber passes). Building a huge carrier fleet is also pretty much a surefire way of beating the AI(it has no clue how to deal with mass bombers).
Disciples, Defense Vessels, Carriers loaded with fighters, and Illuminaters will more often be early game workhorses or built as counter-units.
Iconus Guardians are key to any late game advent fleet. Grab 3-5 of them in a fleet. You should really manually cast both their abilities(not so hard to keep up with as you basically just need to order a new shield projection every 30 seconds and situational Repulses). Repulse also synergizes a great deal with Carrier Fleets, allowing you to keep enemies away from your carriers
Also don't bother with the Domina Subjugator at all if you don't want to manually cast it's abilities. It's not really a "necessary ship to the advent's strategy in general due to how unwieldy it is at the moment.
Also I may as well touch on capital-ship composition: For the Advent both the Revelation Battlecruiser and the Radiance battleship are considered to be rather weak and generally are only built when the interrupts they provide are needed. If you want raw firepower grab a Halcyon- all three of it's abilities are amazing and the extra squads of fighters mean it has way more firepower then the radiance.
The Rapture is primarily a late game ship- so your main early game ships are progenitor and Halcyon.
You only need one Rapture- but in super long games a second mothership is goo, and more Halcyons are always useful. Radiance may be a niche counter-ship you build occasionally when he enemy has a particularly troublesome capital ships such as a high level marza or Dunov.
Putting it all together:
The Advent is all about synergy and has more ways of mitigating damage then any other faction. Between Iconus Guardian's shield projection(and eve in long fights you should ALWAYS make sure some guardian is projecting it's shields at all times), Vertigo on the Rapture, the advent's high shield mitigation, and the progenitor's shield regeneration enemy fleets will often find it difficult to put a dent in the advent fleet(except for the vasari- they cheat with their shield-ignoring phase missiles).
Meanwhile the advent fleet uses it's primary damage frigates coupled with their respective auras they benefit from to dish out a ton of damage(concentration Aura from the Rapture buffs carriers/bombers and Energy amp Aura from the Halcyon buffs Destra crusader damage output).
However between Auras, regenerate shields, and Guardian shield projections you generally want to keep your fleet in tight formation so that all your ships are close enough together to benefit from each ship's AoE effects. This gives rise to the so called "battle-ball" formation Advent fleets tend to take. This often means you want to have your fleet set to "hold position" and need to be careful to not let any of your ships chase enemies alone and fall out of formation.
Anyway that's all that immediately comes to mind on advent fleet tactics, hope some of it is useful.