Copied MIDI doesn't follow the tempo

Hey there! I’ve been using Cubase for ages but never had this annoying issue before. I’m trying to copy midi notes (from a piano roll, not the events on a track) from one project to another. The project I want to paste them in is active, and the one I’m copying from is inactive, the projects have different tempi. When I paste the midi notes into the new project they don’t follow the tempo, i.e. don’t stick to the grid. All tracks are switched to Musical Time Base, and grid snap is on. I’m 100% sure it used to work fine. And I’m pretty sure it still works in other projects, so it might be some setting I’m missing. Any ideas on how to fix this?
Note: if I copy events, the midi notes within them are on the grid, though it’s not the way I’m used to do it nor it is convenient for me.

Hi,

This sounds really weird. Are you sure the other project is using Bars+Beats grid?

Could you attach a screenshot, please?

Hi, Martin!
Yes, the timeline everywhere is switched to Bars+Beats, and the grid uses quantize.

This issue occurs only when I copy midi to this particular project. Interestingly though, it doesn’t when this project is inactive.
When I copy the same beat to another project, or any other midi in any other combination of projects, it works fine (though it usually pastes to a different place, not the cursor, but it doesn’t matter as long as the notes are on the gird, which they are).
So it all makes me think that the issue is somewhere in the problematic project itself.

The first screenshot is the beat in the original project, the second - when it’s copied into the new one, the third - grid settings of the project (as far as I can see, they’re the same as other projects)