The question is quite complex, as we do not have definitive evidence on what language the troops would have spoken. However, with the available sources we can take fairly reasonable guesses based on the military campaigns and the sourcing of the troops.

First things first, the most detailed sources on the Muslim conquest of Hispania are quite noticeably late (second half of the 9th century, so over 150 years after the facts), and very heavily riddled with legitimist umayyad propaganda, so we have to take them cum grano salis.

The source closest in time to the facts is the Continuatio Isidori Pacensis, also known as Chronicle of 754, or Continuatio Isidoriana. This is from 40 years after the conquest, so it would be within reasonable time, within living memory, with people still alive and remembering more or less well what had happened. Here we can read these words: nam aggregata copia exercitus adversus Arabes una cum Mauris a Muza missis[...]. King Roderic is said to have gathered an army against the Arabs joined by the Moors sent by Musa.

So, here we have an important distinction: Arabs and Moors. Indeed, there were both Arabs and North-Africans in that army, but the Moors would have been the highest force by numbers. The Arabs were the commanders, the high officers, whilst the troops and qaids would be Moors or Berbers. With the terminology we run into another problem. Mauri would be the inhabitants of the Mauretania, who are normally equated to moors or berbers, but it would apply too to the Mauro-Romans, the heavily romanised berbers, and the exiles from the fall of the Exarchate of Africa who moved Westwards, establishing themselves in romanised places like Volubilis, Nekour, Ceuta, etc.

These troops were also joined by the last remnant of the Exarchate, count Julian of Ceuta. This Julian was governor of Ceuta in the year 685, when the Byzantine emperor offers troops to the pope, and one of the armies he mentions is the exercitus septencianus, commanded by count Julianus who could offer half a dozen drommons. With the fall of the Exarchate of Africa, Julianus was left entirely alone, commanding Ceuta and having the neighbouring berber tribes as vassals, clients, or under his protectorate, that's why he is referred to as "king of the ghomaras" by Ibn Khaldun (though the term "king" may not be an appropriate translation, "ruler" would more adequate). Julian's troops would be very romanised and ordinarily speak African Romance or African Latin, as their references would be Ceuta and Tingis, but also the Iberian Peninsula, where the majority of the population would speak dialectal latin or "mixed Latin" as Saint Isidore of Seville called it in the first half of the 7th century.

The troops commanded by Tariq ibn Ziyad would have been locally sourced in the North of Africa. That territory was mostly amazigh-speaking, but there was a very heavy presence of Latin or African Romance speakers due to the romanisation and the large migratory movements caused by the Islamic conquest of the Exarchate. Refugees from the kingdoms of Altava, the Dorsale, and the various Mauro-Roman kingdoms moved to the Mauretania Secunda and Mauretania Tingitana. Some names do come up as very Roman when you dig just a tiny bit: Kusaila or Kasila was none other than a Mauro-Roman named Caecilius.

In the North of Africa, mostly both of the Mauretanias, there was a very long linguistic coexistence of African Latin and Amazigh, and it is very well attested in the loanwords present in the latter, an element very well analysed by Brugnatelli in 1999. Bear in mind too, that in the first century or so after the Muslim Conquest of Northern Africa, ARabic would not have substantially permeated the Berber culture, and Arabic language would have been limited to urban areas and the aristocracy.

Logistically speaking, it also makes sense to have the vast majority of your troops speak the language of the territory you are trying to take over, which would have resulted in a preference for African Romance speakers over Amazigh speakers.