Ok first the setup: I start with LR Classic (in a shared album, smart-previews in the cloud) and send a RAW to Photoshop, after I'm done with my edit the saved tiff gets added my LR classic and automatically added to the shared album as a smart-preview too (thats nice).
In LR Mobile I can see my edit in develop mode and in the preview, so far so good.
Then later I continue working on that tiff (sending it to Photoshop via LR Classic again, so LR gets the update). And it does get the update, LR classic shows the changes I have done.
Back to mobile, here I get the old version in develop mode, the preview thumbnail gets updated to the new version, if I open the tiff smart-preview into activity, rating, or info view, I see the updated version as it should be.
But if I get into develop mode in LR mobile, it shows the current version (as it should be), but only for a second and then switches to the version that was first shared when I saved the first edit (that is now outdated and not what LR classic shows or whats actually in that file).
If I switch from develop to the activity, rating, or info views it remains the incorrect older version, If I get back and go into activity, rating, or info view directly without going through develop, its the current version as it should be again.
Biggest problem, on export I always get the old outdated version of this photo, even if I don't export out of the develop mode view.
With Store Album Locally enabled, I can duplicate this. I will log a bug with the Android team. Thanks for the report. As a workaround: You can unsync the file from Lightroom Classic Allow the sync to update on the Android device Resync the updated file from Classic.