You search for them, because nothing will bring them to you. Instagram notifies you when someone links your account with an @ and in no other case. A caption that types your brand name as text, or a photo of your packaging with no words at all, creates no notification and never appears in your Tagged tab. It is not hidden. It is just not addressed to you.
Why the good posts are the untagged ones
Somebody who tags a brand usually wants something from it: a repost, a reply, a gifting relationship. Somebody who names Olipop in a caption about their fridge is talking to their friends, and the can is scenery. That second post tells you what people say about you when they are not addressing you, which is the more honest of the two and the harder one to obtain.
It is also the one your competitors are not reading, for the same reason you were not: nothing put it in front of them.
The four strings to search
A brand is named in captions by more than one string, and searching only your handle is searching the smallest of them.
Search the brand name as a hashtag. Search it with the space removed. Search your best-known product on its own, because plenty of people name the product and never the company. And search any nickname customers invented, which you will only know by having read enough captions to notice it. Then search the name as plain text rather than as a tag, which is the step that catches the caption that never used a hashtag at all.
What breaks when you do this by hand
Hashtag results are ranked and truncated. You see recent and top, not all, and a post from three weeks ago is effectively gone. So the manual search is good at this morning and useless at last month, and worst of all it fails silently: there is no message telling you how much you did not see.
That is the real argument for automating it, and it is a narrower argument than most tools make. The problem is not that searching is hard. It is that searching only works forwards, and the question you will eventually want to answer is what happened while you were not looking.
The honest limit, ours included
No text search finds the post that shows your product without naming it. A can in the corner of a photo, a bottle on a shelf behind somebody, your packaging visible and never typed. That post is a mention in every sense except the one a search can reach, and any tool claiming to catch all of them, including anything we would sell you, is overstating what text can do.
What is checkable is the named half, and it is bigger than most brands expect. The Dr. Squatch page is public and shows the posts themselves rather than a number, which is the fastest way to see what a month of untagged mentions actually looks like before deciding it matters.