Under Linux the upgrade would be controlled by your distribution looking for upgraded packages, presuming you’re not using the tarball version (which it sounds like you’re not, since in that case you get a popup window telling you about the new build that takes you to the download page).
As a result of the community backlash, the update dialog has been reworked to make this more clear, as seen below. This particular update is the first one in Sublime history where the user base rose up in complaint, even though the upgrade from ST2 to ST3 behaved the same way.
From the purchase page:
Current currency conversion from USD to Eur:
Thus, the perceived per-year cost of a license is 28.45 eur, assuming that at the end of the three year period you decided to purchase another 3 years updates. If not, you could continue to use your copy of sublime in perpetuity, in which case your per year cost declines as time goes on.
In any case, while we all recognize that the situation is less than ideal and disruptions to tooling is unpleasant, please try to keep your language civil and profanity free.