The tape monitor button is for listening or monitoring the sound coming from the tape deck. Unless there is a record out button or selector on your preamp the tape out jacks will supply a non volume controlled version of whatever the pre amp is outputting.
When you say you can "play a tape through tape 2 out at the same time as listening to the cd through the headphone amp" do you mean that you are hearing both the cd and the tape together on your headphones? If so that would be expected as the tape out 1 and tape 2 out on a preamp are usually in parallel so in effect they are acting as a "Y" cord and combining the two sources. Move your tape deck output to the tape 2 input on your pre and you'll be fine.
When you say you can "play a tape through tape 2 out at the same time as listening to the cd through the headphone amp" do you mean that you are hearing both the cd and the tape together on your headphones? If so that would be expected as the tape out 1 and tape 2 out on a preamp are usually in parallel so in effect they are acting as a "Y" cord and combining the two sources. Move your tape deck output to the tape 2 input on your pre and you'll be fine.