/sic' / सिच्ऽ

The root sic' सिच्ऽ means "moisten, sprinkle".

Not the same thing as the affix /sic.

/sic' makes the a-aorist **asicat असिचत्.

/sic' + /luG
→ /sic' + /sic + /luG
→ /sic' + /aG + /luG
→ **asicat असिचत्

evam uktas tu saumitrir abhyaSiJcad vibhISaNam |
madhye vAnara-mukhyAnAM rAjAnaM rAma-zAsanAt ||
"Thusly addressed, lakSmaNa sprinkled vibhISaNa as king of laGkA
in the middle of the monkey generals, as per rAma 's command."

Hm. Shouldn't that "sprinkled" be "anointed"?

No, for anointing you use ointment, or at least olive oil. vibhISaNa was sprinkled with holy water.

How come abyaSiJcat got /Satvam even though /aT came in between /abhi and /sic'?

Today I'm out of aspirin, so I'll leave the finding out the small details as an exercise for the diligent student. The broad reason is BSSSS.