On the one hand, I don’t have any money and on the other hand, I also don’t have the time for it.
In this sentence, “zum” is a contraction of “zu dem” and is used to introduce two contrasting points. “Zum einen” means “on the one hand” and “zum anderen” means “on the other hand”. “Dazu” is an adverb that means “in addition” or “to that”. In this context, it refers back to the previous point about not having money and adds that the speaker also does not have the time.
I think that this is a slight misunderstanding of the “dazu”.
It does not refer to the first part of the sentence, but it means in this case “for it” referring to something in context but not at all in the sentence,
“Gehst Du zu den Rolling Stones im Hamburg?” Nein, zum … … dazu." (dazu = um da hin zu gehen).
What you mean would be “zudem” (= furthermore) but it would not make sense in this sentence because it would kind of double the “zum einen … zum anderen”.
You could say
“Ich habe kein Geld und zudem auch nicht die Zeit (dazu).”
First, I don’t have any money. Second, I don’t have the time for that.
What you’re explaining doesn’t change the fact that the translation given is poor at best and just wrong at worst. “For one thing, I have no money and for another, I also don’t have the time for it.” ← As per the the Explain button or the highlighting of the sentence on this very app.