As far as I know the initial design calculation for teams joining a league in the break between seasons is based on their active CD (level, strength and weakness) and the number of races in the next (upcoming) season.
So where a league moves from say 15 races to 20 races all of the established teams will have had their initial design built up over the previous 15 race season as per this guide...
Start of season car design (Elite)
The newly joining team will have their design based on the next season 20 race series so will have a much better initial design than the remainder of the teams. A 20 race series will give them 50dp in every attribute except CD weakness whereas the established teams will only have 38dp.
Currently the only fix for this is that all of the established teams would have to leave and re-join the league so that their initial design would also be based on the upcoming 20 race season.
A similar problem will arise if a league reduces the number of races. But in this case the newly joining team would be disadvantaged because their initial design would be based on fewer races than the established teams.
The devs could fix this by changing the calculation for newly joining teams, calculating their initial design from the number of races in the previous season instead of the next (upcoming) season. I have suggested this to the iGP team but have no idea how difficult it would be to code so don't hold your breath.