unless You have animated mesh sequence, then particle instancer on its own have no effect on animation offset.
It depends on effect's complicity, but if simple, then I'd rather create character for each tentacle and use animation clips with offset to animate others.
Also, if no Trax culd be used and tentacle's animSetup ir relatively simple, then expression could be written to start animate each tentacle at frame given individually. Here particle could be usable to set this startFrame and pehaps agePP for individual scale.
I'll try to figure out anything else or more precise, and if successful I'll post it here.