Yes the number behind the dot is the tiebreaker.
About the GEOLOGIST tile:
The rule text written at that Goal tile is:
"Most complete sets of all terrain tiles.
If tied: player closest to completing their next set."
I would interpret "closest to completing next set" as having 3, 2, 1, or 0 different land types among the tiles which aren't part of the complete sets of 4 land types. I now see Harry counts the number of sets of 3 land types among those remaining tiles? We will check if that's the best interpretation.
BTW: In my version 10 years ago the rule in the rulebook was:
"Who has the most of the 4 different landscape types?
In case of a tie, the tied player with the most sets of their landscapes (2 of each, 3 of each, etc.) wins."
The new edition text maybe reads easier, but in case all players have all landscape types it makes in fact an extra tiebreaker which is not so easy to see in a large tableau.