Explorers these days have it "easier" - in the sense that there are now plenty of remote outposts scattered throughout the Galaxy, where an explorer can stop and sell off data if they wish. You no longer have to travel all the way back to the Bubble just to claim your Tags.
But yes, you don't get the Tags unless and until you sell the data, and if someone else happens to scan the same system and beat you to it in getting back and selling the data first, then they get the Tag, not you.
Of course, it's entirely possible that before you came along, someone else had already visited and scanned the system you're talking about, they just haven't gone back to base with the data yet. If they did, they might sel their data tomorrow, they might not sell it for months. There's simply no way to tell. Either way, first-to-sell gets the Tag.
Finally, I should also point out that if your ship explodes, you lose any unsold exploration data on board and you won't get the Tags - so don't die.
Remember, Sir Edmund Hillary and Tensing Norgay almost certainly weren't the first people to climb Mt Everest. But they were the first to do it and then come back alive with proof, so they get the credit.