Flats newbie.....ringing after release?

[big_z_in_miami]

Experimenting with flats (on my Pbass) and finding that they tend to ring after I lift off the fret but still muting with the left hand. The strings, particularly the A string rings slightly unless I mute with the right hand also.

Is this common with flats, or just new flats? Is this why folks talk about adding a mute (foam) at the bridge?

Or is it the nature of the higher tension strings (my flats are super tight) and you need to be more aggressive about muting?

Got to admit....I added a foam piece at the bridge and really liked the serious motown sound, but the sustain can be too short for some of my songs to use it that way all the time.