TL;DR
>DARKSOUL invasion/invocation mechanic instead of isekai shit
v2.0

>RULES
- First drift happen randomly under great emotion
- Drifter self-world remain time-frozen (plot-critical)
- Drifter world is Self-world, Others' world are Host-world
- Outsider(s) drifter always appear as (retconned) people with fitting 'advantage'
- Drifters & Host can drift to any drifter they once meet in a world
- Drifter & Host can always feel each others presence
- Drifter is forced to stay in the world as long as the Host feel in danger (or remain alive)

>STORY
MC was told by his father he might inherit his family "drifter ability"
MC first drift happen during a catastrophe
MC come back, is saved from getting killed by truck by the one he helped (who appeared as an heroic fireman), his father recognize the sign he drifted.
MC start making friends by answering other-world call for help (be it invocation by a princess or an orphan puppy)
MC discover the EVIL-drifter, who keep killing Host everywhere he appear
MC lose a best bro
Back home, MC suddenly feel the E-drifter appearing in his Self-world to kill him
MC panic
All his friends answer the call (even the ex-puppy, now a bear, yes)

>TWIST
MC realize Evil-drifter is desperate, always trying to delay returning in his own shitty world
Everyone can feel Evil-drifter call for help but cannot join him because he keep drifting (time-freezing his world)
MC manage to convince E-drifter to bear it and wait for help
MC feel safe again
E-drifter finally leave on his own
MC answer his call for help
Turn out E-drifter's host-world is in interstellar war and they torture their drifters to attract/harvest outsider drifters for energy (plural = distinct timeline).
MILLIONS of drifters have answered E-drifter call
GLORIOUS BATTLE FOR EVERYTHING (MC is but one elite space-marine, that princess command a frigate, E-drifter is an alien octopus)

Happy end.