There is a good chance that you are seeing Limping syndrome caused by Calicivirus.
Calici is a virus that usually causes upper respiratory infection in kittens but some strains also can cause the type of lameness that you are seeing. They could have contacted this virus at the shelter or it is also possible that they can develop this syndrome in response to the vaccine if a modified-live vaccine is used (this refers to how the virus is made - vaccines can either be modified live or killed virus). The lameness and fever generally runs its course in 3 to 5 days. You may ask your vet about giving an anti-inflammatory for the fever and pain, but do NOT give anything without specific instructions from your vet as cats are very sensitive to many medications. Because this is a virus, antibiotics are not effective against it.
There are other infections (such as Mycoplasma) that could also cause this, but Calici virus is the most likely cause.
It is not very likely that your adult cats will come down with this, especially if they are up to date on their vaccines, but since there are several strains of Calici virus, you can never be 100% positive that it will not be transmitted to them.
Please let me know if you have additional questions.