Neither the character sheet nor skill DPS tool-tips will update until you reequip your weapons, however there’s an even weirder behavior that I haven’t seen anyone post about. While the character sheet won’t update the first time you assign the passive, it will however update when you respec and take the point out of the passive node, but not in the way you’d expect. When respeccing and taking the point out of Critical Precision, the character sheet will automatically update but actually show a higher crit chance, and the DPS tooltips will show higher DPS as well, specifically the numbers that you should have been seeing when putting the point in in the first place. Adding the point back will show a dropped DPS and lower crit on the character sheet, and you can repeat this cycle as much as you want.
Once you swap a weapon out and in it’ll update the character sheet and tool-tips.