Actually Katakana derived from Kanji, but were typically only used for their sound rather than their meaning and a very very simplified version of how you would write the character quickly allowing for lifting the brush (Hiragana is the simplified version quickly without lifting the brush) roughly speaking; so you are mostly right but not completely.

シ comes from the Chinese character 之, meaning either "of" or "this"

ツ comes from the Chinese character 州 (although some researchers disagree), meaning "state" or "province"

ソ comes from the Chinese character 會, meaning "meet", "party", or "interview"

ン comes from the Chinese character 尓 (again not clear), meaning "you" or "that"

This divergence happened because Chinese characters were used to write Japanese which is mostly from a different language family. Some Chinese characters were used by some for their meaning (ideogram) and used by others for the sound they made to approximate the sounds used in Japanese. Obviously Chinese influenced the Japanese language (for example numbers in Japanese sound similar to numbers in middle ages colloquial Hokkien). Over the last 1,000 years or so there have been numerous occasions for changes, standardisation and simplification. So even to those who study these changes over time it can sometimes be unclear.