"Here are the cars they tested."
Translation:Voici les voitures qu'elles ont essayées.
Yes, agreement is with the direct object as it precedes the compound "avoir" verb so qu'ils ont essayées should be accepted.
Essayé means "tried" not tested. If you wish to communicate they took a "test drive" you should say so. Otherwise tested means they performed tests on the cars. Testé or fait analyse should be correct.
Adding sont would be somewhat redundant, as voici translates to "here are," I believe.
Why isn't the verb 'tester' correct also, after all the sentence stipulates testing not trying?
The verb essayer is correct but, it is required to be written in passé composé and, in that tense essayer uses the auxiliary verb "avoir ".
There is generally no agreement with avoir compound verbs however, because in this instance it is preceded by the direct object, "voitures", the past participle must agree in gender and number with the DO.
Therefore, it must be essayées as the direct object is feminine and plural.