First off, the air you are getting in the tube is NOT the air that comes from the lines, but most likely is the air you get at the bleed screw. There are two places you can get air at the bleed screw. One place is where you put the tube on. Another place is through the bleed screw treads - that's because you unscrewed it 1/4 turn or so, and the special grease which seals the treads is probably gone, and that's why small amounts of air sip in as you create vacuum.
If you bled for a while, close both bleed screws, and see how the lever feels. If it's pretty hard once you apply pressure and is not spongy, then in all the likelyhood you are perfectly OK. Zip it up and you are done.
Now, I don't know why you are bleeding the brakes. If by any chance your system was completely empty (like after rebuilding the caliper), or partially empty like after changing the brake lines (and you got some air in the calipers), the mity vac may not be able to get rid of pockets of air in the calipers. Naturally, you will know about this by the lever being very mushy. The only way to get rid of air in such case would be to bleed using the traditional method - open the bleed screw, squeezing the lever, close the bleed screw, release the lever, etc.
I would strongly recommend to get and install
fast bleeders (plenty on ebay). This way bleeding becomes a piece of cake because fast bleeders have a one way valve in them. So, you just add the fluid to the reservoir and keep pumping. As the level goes down you add more fluid and keep pumping. After a few cycles you are done. I would like to point out that if the system was mostly empty, you can't start with fast bleeders - not going to work. In this case, mity vac is the only way to conveniently fill the system besides the traditional method.