"Those are not my spiders."
Translation:To nejsou moji pavouci.
Could we say "ti nejsou moji pavouci" to convey the same meaning? Or "to" is used exclusively in such sentence constructions? I suppose, demonstrative pronouns only match the gender/number/case of a noun which they directly precede, as in "ti pavouci nejsou moji", translated as "those spiders are not mine".
No, in this case using "ti" would be incorrect. The sentence is similar to those you have learned at the beginning of the course (To je muž.; To jsou ženy.; etc.), in this sentence there is only more information that you have to put together. This sentence also uses the phrase "to je (for singular)/to jsou (for plural)", only this time it is a negative phrase "to není (sg)/to nejsou (pl)". The phrase is commonly used to identify nouns (gender of nouns does not matter, you only adjust the verb to be in singular or plural).
Now if you used the simplest sentence - "To jsou pavouci." = They/Those are spiders.", the sentence would definitely remind you of something you already know; adding negation - To nejsou pavouci. They/those are not spiders.; and the pronoun "my - my spiders" used in the correct grammatical case. - To nejsou moji pavouci.