It's pretty clear that companions that are left at Spire are leveling up even though they are not traveling. Not sure what the mechanics is but I can confirm.
There is an interesting bug though regarding "ranks trained this level".
In my case, Verse was left at the spire at level 11. When I came back, she was level 12. I save at the entrance to spire.
If I remove Sirin and add Verse, and then go to trainer, I see that she has 0/5 ranks trained this level and I can train.
If I reload, remove Lantry and add Verse, and then go to trainer, I see that she has 5/5 ranks trained this level. Though ranks are not higher than in the first case.
What's going on?
There is an interesting bug though regarding "ranks trained this level".
In my case, Verse was left at the spire at level 11. When I came back, she was level 12. I save at the entrance to spire.
If I remove Sirin and add Verse, and then go to trainer, I see that she has 0/5 ranks trained this level and I can train.
If I reload, remove Lantry and add Verse, and then go to trainer, I see that she has 5/5 ranks trained this level. Though ranks are not higher than in the first case.
What's going on?