It actually defaults back to the current class of character selected for character filtering.
eg: Select an Assassin character, then change the character filter on the left side for characters to Sentinel (do not click on another character). Go into talismans for the Assassin character and it will default to Sentinel talismans, unless you select a class-specific talisman slot.
Basically, the character type filter is being inherited by the talisman filter.
If you don't select a character filter, the default is "all" which equates to "cosmic" in talisman terms.
Note:
- Equipping direct from another character bypasses that filter it seems.
- Regardless, it always resets to the start of that selected talisman filter when you choose a new talisman slot.