Specs show your Trek was equipped with double wall rims. If the rim strip was the typical thin, soft, flexible rubber band strip, it won't provide enough support.

Are the holes on the inside facing the rims, rather than outside facing the tire? If so, check for dimples in the tubes that correspond with the spoke nipple holes in the rims. The tube is extruding through the holes in the rims because it doesn't have enough support from the rim strip or tape. Eventually those dimples develop tiny splits and slow leaks. If it happens once it'll keep happening.

As Clyde1820 suggested try some better rim strips or tape. Any cloth tape is good -- Velox, Nashbar or others. These cloth tapes are fairly thick and use a tacky adhesive so the tape can be repositioned easily yet holds securely.

Or stiffer high pressure rim strips from Schwalbe or others -- they'll be marketed as high pressure or HP rim strips or tape.

Some folks say ordinary duct tape works well too. Wrap around the rim holes two or three times, depending on how the tires fit the rims.

If the rim strips or tape are too wide it can interfere with seating the tire bead. If that happens trim the tape a bit narrower, or buy a thinner rim strip/tape. If the non-adhesive rim strip is too narrow it can wiggle around and leave the tube unsupported. So Schwalbe recommends using the widest HP rim strips that will fit inside the rim without interfering with seating the tire bead.

I've used 16mm Velox and Nashbar cloth rim tape on both my hybrid's 622x19 double wall rim, and on my road bike's very narrow 622x14 rim -- the rim's concave curve ensured the 16mm tape wasn't too wide as long as the rim surface was clean. The other rim has some residue from old rim tape that interfered with seating so I had to use 12mm wide cloth tape.