3 way switch terminals
First off please be aware that the non-contact voltage tester will test for voltage present not current. When you have only the feed wire connected to the switch there is NO current flow at all.
The non-contact voltage tester can be triggered by adjacent conductor coupling where one conductor has a voltage present whilst the other is open. Inside your switch one position clearly puts internal metal parts in closer proximity that in the other position. The closer connections are allowing the coupling to the unconnected terminal making it appear that it has voltage present. This is one reason you need to take careful analysis of what a non-contact voltage tester will detect or not detect. To be honest it is better that the tester shows a voltage coupling than not so you have to pay close attention to what is going on.
Any conductor that is tied back via the neutral or safety ground connection will not be detected by the non-contact voltage detector because the wire is not open (i.e. has a low resistance path to the circuit return) and thus is not going to be subject to any possible coupling from a hot circuit conductor.
A non-contact voltage tester can be a good first level detection method. And it is normally recommended that before committing to its use each session to use the detector on a known powered circuit and one that is not just to make sure the thing is operating correctly. Beyond the first level detection there are other pieces of equipment that can give a more concrete circuit state determination. One of these is to use a digital meter. Note that a digital meter may still read a voltage on coupled conductors but normally a much lower level voltage than a conductor with a real voltage connection.