Vitamins should be just fine, but be aware that the medication question on the medical app asks about "any medication, prescription or non-prescription"

So what exactly is a non-prescription medication? Only something approved by the FDA? What's the line between medication and supplement? It's not clear. Would the FAA care about vitamin C? No. Would they care about the herbal supplement St. John's Wort, which is commonly used to self-treat mild depression? I'm betting they probably would...

Precedent has shown you can get away without reporting common vitamins. Beyond that, who knows?

As far as DOT drug tests, those only detect specific drugs which are commonly abused to get high, ie the usual narcotics, weed, and maybe a couple others. They don't detect medications or supplements, except for meds which happen to contain opiates (ie cough syrup).

So the concern is not drug tests, but what would the FAA think if they found out which is not likely in the case of run-of-the-mill supplements.

Although one airline pilot was recently incapacitated in flight because he took a bunch of a vitamins on an empty stomach so don't do that.

If in doubt it wouldn't hurt to ask your AME. The FAA does have a list of flight-approved meds which you can find online, but that is not intended for pilots to circumvent the AME since the underlying condition might be of concern even if the medication is not. But the list is a good for things like cold medications, some of which are non-narcotic but can still make you drowsy. Generally you need to try any new medication, including FAA approved meds, for a period of time before flying just in case you have a bad reaction.