Haha, I'm going to get to that part in the guide but whoever said phase by phase is in fact correct. There are special exceptions though.
However, you want to minimalize this to 2 swaps only in boss fight instances if you will do it..
So lets use T13 for example.
P1 and P2 you would use Ifrit.
P3 - You will use both. Garuda is the better for AoE here BUT there are limits of when to actually make the switch to Garuda. Lets say we have a few mobs next to each other. If you were to apply a set of DoTs onto one mob and bane them onto nearby mobs, If those mobs will survive for less then 18 seconds (a full duration of Bio, still use Ifrit. However if they will survive for longer then 18 seconds but closer to 33 seconds in total, use Garuda to maximize the effect on Contagion.
P4 - Ifrit again.
Using what I said for P3, the actual time to switch to Garuda would be slightly before when the Storm of Meracydia finally becomes targetable.
In terms of Dungeons, Garuda will be more useful for mob pulls on average (unless the 18 second rule applies), while Ifrit for bosses.
There's another case like T11, where the add phase requires a magic attack vs a melee on one node, so that's another way a switch will need to be made.
Another case is based off of my last example. In your party composition, if you have other magical DPS in your party who would DPS as well (SCH or BLM) and will beat the DPS of Garuda, still use Ifrit.
Again in T11 for example, If a SMN does not need help to kill the magic node in time because either a SCH or BLM is helping them or the melee is slow enough, Ifrit will still be better here.
*Super special case. T10. So while I said in my second case that the 18 second rule should determine the use of Garuda vs Ifrit, something like T10 actually disobeys this rule. In the case where there are SOLELY two mobs that a pet can hit while there are also multiple mobs more then two on the map, even should Contagion be a thing, Ifrit can STILL beat Garuda due to the 532MP to swap. The add phase but more specifically the given adds, do not last long enough as a whole to warrant the use of Garuda and 532MP, ontop of the fact that Gaurda cannot target more then 2 mobs at the same time. You can infact save the 532 MP to use for your own DPS later and win out here. The special exception to this case would be when Raging Strikes / INT potion DoTs can be baned onto the second target AND it won't take forever to die but at least long enough to take advantage of Contagion.
So basically those are the four exceptions roughly where even should Garuda technically be better in the enviorment, Ifrit will win out.