Some FATEs in Azys are linked to a certain weather (Electricity or something, never had the chance to catch it) and they are pretty short I heard. However I doubt an S rank would spawn "later", all the others are instant ; you step on a landmine, bam Nandi / Brontes / Croak / Mind shows up, you catch a fish, bam Zona / Theda shows up, there was never a "15 minutes later". I don't think it has changed

Regarding Senmurv's trigger, this is what have been done on Moogle with no success at all (still 0 spawn of Sen since EA) :

- Killing chocobos
- Doing hunters FATEs in chain
- Summoning chocobo on a spawn point
- Runing around with a chocobo
- Flying around during cloudy weather
- Steping on landmine with chocobo out
- Killing the bull chocobo fATE
- Killing mark bills in Dravanian Forelands

... and still nothing x_x