I would quibble with that on a couple of counts. As far as I know, the standard reading for those characters is 'sumi-tsuke'. I've just searched online, and in my two kanji dictionaries, in vain to see if there is a variant reading of "sumidzuke", to no avail. I'd be interested to see a link to a dictionary where that kanji pairing is written in kana as "sumidzuke".

As for a literal reading of the characters, while there is a Sumitsuke Festival at New Year's in certain parts of Japan, in which people blacken their faces with ink, the literal meaning of the two characters is 'ink-apply', i'e., "put ink on (things)", not "blacken the face". Neither character in sumi-tsuke means 'face' or 'black(en)'. Sumi is ink, and ~tsuke is apply, put on.

The common (i.e., not literal) meaning of sumitsuke to people in Japan, according to standard dictionaries, is in reference to the New Year's Festival and people blackening their faces. The meaning of 'putting ink on timbers' is a secondary meaning and one of those technical carpentry words known to fewer regular Japanese folks.