Tapping problem?

Do you play unplugged? If you tap your electric bass unplugged, you will hear the notes from both sides of the fret (i.e. if you tap at the 12th fret, you will hear the note between the 11th fret and the nut as well). If you play through an amp, only the intended note is supposed to get heard. It may be something else though.

 

It's nothing wrong with your technique. Tapping divides the string into two parts, both of which will ring. However, since the pickups only sit on one side of the stopped string, only the note you intend to play will (usually) be amplified.

If you have an unusually sensitive instrument, you can prevent the "wrong part" of the strings from sounding through the pickups by muting them with a scrunchie/hairband near the nut, a la Victor Wooten. Or you can stuff tissue under the strings there.

 

You may want to record some tapping that you do to make sure that indeed it is just from your bass and not your amp. i know that when i first started learning to tap i heard a similar thing and it was the harmonics that were ringing out as well as the intended note. in my case this turned out to be because i wouldn't hit the note with enough confidence(as well as getting the proper position without my finger fattening up over the fret). When i just go ahead and lay into the note as if it's going to come out clean and clear, it does.