No it's not natural and has nothing to do with the season.
It could be any number of reasons. They could be catching their tails on decorations you may have in the tanks, they may be having their tails sucked into the filter ( if the filters are not sponge types or protected/modified cannisters ) it could be a disease such as fin rot, they may be biting them out of stress....
Answering the following questions will help to find out what the cause is, so we can help and advise.
What size and set up of tanks do you have?
How long have they been set up with the fish in them?
Are they cycled?
Do you have filters and heaters in both tanks?
What is your water change regime? ( how often and how much do you remove )
If you can also provide a clear picture of each fish and it's tail, this will also really help.