Am I right in saying that the verb has to match the tense of the il y a construction?

No! That is fundamentally wrong!

Two conjugated verbs! That implies two propositions! Each one having its own meaning in a given time reference => Each to its own! Each one its own tense!

Because, if the two propositions are part of the same sentence, one could assume that the two propositions are in some way related. Some logic is supposed to govern that particular relationship.

That particular logic will then force some concordance between the tenses expressed by the verbs. Concordance meaning that they are both compatible. Not necessarily identical.

If I need to say that Hic & Nunc I can assert that there are (Hic & Nunc) FSE contributors who, nachdem will comment this answer, I can write that :

Il y a sur FSE des contributeurs qui commenteront…

Those translations are all correct except for the last one, which should be sommewhat different; that is, as written, it is not quite correct.

• There would have been people eating if we had arrived earlier.

• Il y aurait eu des gens en train de manger si on était arrivés plus tôt.

In a continuous tense the sense of the verb “manger” is different, more “factual”.

• À midi il aurait mangé et non pensé à aller se coucher. (prendre un repas)
  At twelve he would have [eaten/had a meal] and not have thought of going to bed.

• À midi il aurait été en train de manger. (action de mâcher et d’avaler de la nourriture)
  At twelve he would have been eating.

However, “prendre un/son repas” is also used in a “continuous tense fashion”, that is with “en train de”, a locution saying that the action is going on at the time referred to.

• Ils étaient en train de prendre leur repas à la terrasse d’un restaurant.

No, you are not right to think the tense of the verb has to match necessarily the tense in the “il y a” construction, unless you understand that “il y a” is used to confer coincidence in time. To cite the TLFi (IV A), “il y a” is used as a “morphème de présentation” but we should say rather “il y a/il y a eu/il y avait/ il y aura/il y aurait/…”; what is presented to the interlocutor exists at the time conferred by the tense or exists hypothetically. “Il y a” means roughly “there exists“. There might not be a coexistence then of the situation or thing claimed to exist at a particular time and the action that is related to it; in that case thes tenses can be different. I won’t list all the possibilities below as I feel unsure about some of them.

• Il y avait beaucoup de téléphones qui sonnaient. (coincidence in time in the past)
• Il y a beaucoup de téléphones qui sonnent. (coincidence in time in the present)
• Il y aura beaucoup de téléphones qui sonneront. (coincidence in time in the future)
• Il y aurait beaucoup de téléphones qui sonneraient. (coincidence of hypothetical situations)

• Il y a beaucoup de téléphones qui sonnaient (toute la journée en ce temps-là). (The phones do exist now and at least in the past they were ringing.)
• Il y a beaucoup de téléphones qui sonneront. (The phones are here now, but they are nog going to be ringing necessarily now.)

No sense seems to fit these constructions.

• Il y avait beaucoup de téléphones qui sonneront.
• Il y a eu beaucoup de téléphone qui sonneront.

It is only needed now to change the type of the verb “sonner” and instead of an action consider a state: “sonner faux”. When you use this verb you do not state an action and more than one tense is possible.

• Il y avait des mots qui sonnent/sonnaient faux dans son parler.
• Il y a des mots qui sonnent/sonnaient faux dans son parler.
• Il y aura des mots qui sonnent faux dans son parler.
• Il y aura des mots qui sonneront faux dans son parler.