I'm looking for a word that means "something must occur with another thing"

You could use requisite in the following way.

Tomatoes are not requisite for a proper salad.

The adjective definition is:

required or necessary for a particular purpose, position, etc.; indispensable:

with the noun form referencing that:

something requisite; a necessary quality, thing, etc.

You have the answer in your question!

Immigration from our Southern borders and crime do not necessarily go together.

Sanctuary cities don't necessarily facilitate drug problems and prostitution just because they do not question immigration status.

Forget about the sample sentence with the tomatoes. Several words, for example, obligatory, could go in the blank, but they wouldn't help you with your real concern.

Try concomitant.

Defined by Merriam Webster as:

something that accompanies or is collaterally connected with something else

Also see below the definition by Cambridge dictionary.

something that happens with something else and is connected with it

Tomatoes are not vital/essential/indispensable in a salad; salads don't have to have tomatoes.

ODO:

vital ADJECTIVE

1 Absolutely necessary or important; essential.

‘Each player assumes a specific role that is vital to the overall team framework.’

essential ADJECTIVE

1 Absolutely necessary; extremely important.

‘fiber is an essential ingredient’

indispensable ADJECTIVE

Absolutely necessary.

‘The horse is an indispensable character to most stories of Chinese warriors.’

I'm looking for a word that means “something must occur with another thing

It depends on the viewpoint and whether there are dependencies at work. Your title, sample sentence, and context are all different in these respects. Salads don't depend on tomatoes - tomato isn't obligatory.

In you immigration example, It appears you are trying to argue that crime and immigrants don't go hand in hand. Unlike the salad, you are looking at the situation from an outside perspective.

If you want the analogy to succeed, I think you need to make it more parallel to the actual situation so as not to open yourself up to counterarguments in the debate.

obligatory

1: binding in law or conscience

"Obligatory." Merriam-Webster.com. Merriam-Webster, n.d. Web. 17 Feb. 2017.

go hand in hand

if two things go hand in hand, they exist together and are connected with each other (often + with ) Crime usually goes hand in hand with poor economic conditions.

go hand in hand. (n.d.) Cambridge Dictionary of American Idioms. (2006). Retrieved February 17 2017 from http://idioms.thefreedictionary.com/go+hand+in+hand

Prerequisite is what you're looking for!