... so you were punching in, leaving the job, then sneaking in just in time to punch out?
Now, call me crazy, but if I worked the day shift maintaining the computers, I'd get a bit annoyed if I found out the night shift guy snuck out and still got paid for it. If it happened once, I'd ignore it -- how am I to know if he was actually sneaking out, or it was a family emergency and he got permission? But if the night shift guy sneaks out on a frequent basis, I'd be a bit peturbed that he was being paid to do NOTHING while I had to stay in the office all day long and check equipment.
For all you know, someone assumed you had permission to leave the premises if you didn't receive a page, and was asking if they could do the same thing during the day. It wasn't necessarily someone "snitching" ... but heck, I think they'd be perfectly justified if they did.
Turning someone in for dinky little offenses is stupid. NOT turning someone in for larger problems is even more stupid. If you are the computer/tech guy for the evening shift, I assume that there are people who depend on you keeping track of the computers. I spent several months doing something similar -- the company had had a problem with the coolant system malfunctioning, so they needed someone to keep track of the machines on the night shift. Whoever hired you had a reason for keeping you there at night...