Do villains keep leveling if I am on a lower tier?

[Beatum Studeo]

I noticed the villains stay at a lower level for lower tiers. Does the boss still level up on higher tier though? Seems like a waste to use on lower levels and not level the boss but I need to do it to get the lower tier girls. So I was wondering if anyone knew if I am on a lower tier if the villains will still increase in level on the higher tiers? Thanks!

[Slynia]

T = Tier

  Villain     Starting Lvl  Max Lvl(T1)  (T2)  (T3)  Level up(T1)  
- Dark Lord             3           30    80    140     10 wins    
- Ninja Spy             16          50    120   200      9 wins     
- Gruntt                26          70    150   250      8 wins   
- Edwarda               36          100   200   320      7 wins    
- Donatien              45          130   260   400      6 wins    
- Sylvanus              55          170   350   540      5 wins    
- Bremen                70          210   410   640      5 wins    
- Finalmecia            90          260   480   700      5 wins    
- Roko Senseï           110         290   530   770      7 wins     
- Karole                130         310   560   810      10 wins    
- Jackson’s Crew        150         350   615   870      10 wins    
- Pandora Witch         250         500   750   1000     10 wins    
- Nike                  300         550   TBD   TBD      10 wins   
- Sake                  350         600   TBD   TBD      10 wins  
- WereBunny Police      400         650   TBD   TBD      10 wins 

Note: It always takes 10 wins to level up villains at T2 and T3.

 

TL;DR: No, they won't level further once their max level for each tier has been reached, you NEED to fight the villain on a higher tier to further level him/her.