I took one of the "blessing of..." feats that is supposed to give +1 Con and advantage on Con saves. It gave me +1 Con, but did not apply the new constitution hitpoints bonus to levels 1-4 (+1 took me from 17 Con to 18 Con). I couldn't tell from the combat log if I got advantage on Con saves.
For reference, it was a Hill Dwarf Paladin of Tirmar with 17 Con (18 Con after taking the feat).
HP progression was as followed:
Lvl 1: 14
Lvl 2: 24
Lvl 3: 34
Lvl 4: 44
So basically, it started as 1d10+4: +3 from CON, +1 from hill dwarf. The first level is an auto "10" and then 6 (assigned in place of a d10) +4 per level after that.
However, after reaching 18 CON, I should retroactively get an additional +1 hp/level (1d10+5), which means my health should have been 48 at Lvl 4.
Here's the relevant 5e citation:
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