I wouldn't necessarily call it a red flag.
Most jobs require you to support your software. For example, I write bill collection software for the company I work for, and since I'm the sole developer for this particular system, and if the system errors out or crashes at any time, I'm the one who has to fix it.
It can't necessarily wait until the morning when we have 100 agents on the floor during the time they are taking calls, because if the system is down the company is paying those 100 agents to twiddle their thumbs while they wait for me to come in and fix it.
Since going live nearly 4 years ago today, I can count on a single hand how many times I was called in to fix things, but it does happen. The thing that usually sucks about this is that vacation time is usually pretty scare in these environments. I can't plan a 1 week or 2 week vacation in a foreign country where they can't get ahold of me, they will never approve of those vacations. I need to be available at all times.
Edit - As far as tech support goes. We have a help desk line, and a production support team that is supposed to be taking the tech support calls for the system, but typically they just punt (or pass the buck, whatever phrase you want to use) and just forward the crap to me to figure out. So while you aren't taking tech support calls, you are likely to be figuring it all out on your own. For example, this morning one of the client files didn't import into the system, and the tech support came to me "They got this error what does it mean?" "Sephamore timed out" Never heard of that before, I had to google. Oh, the DHCP on the application server was reset due to a firewall being rebooted. But why can't they google the error themselves?... Why wasn't this reboot of the firewall done at a time where the app wasn't processing files? Just bad communication, but that's the things you will run into.