If my opponent has Arcanine ex or Gyarados ex on the Bench, will its "Tera" attribute prevent me from placing damage counters on it with Drifblim's "Curse Spreading" attack?
No, placing damage counters is different than dealing damage, so it won't be prevented.
Source: Scarlet & Violet FAQ; TPCi Rules Team (2023-03-30)

Relevant cards

Note: All applicable cards may not be listed below.
SV1_32
SV1_32
SV1_45
SV1_45
SV1_90
SV1_90