During Festal Matins when the icon of the feast is placed on the tetrapod, what is on the tetrapod beforehand for vespers? Does it just have nothing on it?

Since it is Festal Vespers, the bread, wine, oil and wheat for the Litija are there. Otherwise it will be the usual icon with the Cross and candles (the Cross and candles are always there).

I was waiting to see if anyone else would weigh in on this. In the strict Russian tradition , nothing at all is in the center of the church. The icon is put on the analoy in the center of the church before the Polyeleos at Matins.
Having said this, I realize most Byzantine Catholic and Orthodox churches in the New World don't follow this practice. The OCA parish I serve now has the little table in the center of the church. However, I would wager that in the Russicum the practice I described above is followed.

Here's a video of the Entrance at Presanctified at the Russicum. You can see the arrangement of the chapel:

It would appear in this clip that the analoy is set out for the Old Testament Readings which follow the entrance. I can name two places in North America where nothing is at the center of the church. One would be Holy Trinity Monastery in Jordanville, the second St. Vladimirs Church in Ann Arbor, Michigan.
We must remember that even in ROCOR, Ukrainians and Belorusians tend to outnumber Russians, except on the West Coast. Hence, every ROCOR parish I served had an analoy with the Icon in the center of the temple.

Below is a photo from St. John the Baptist ROCOR Cathedral in Washington, DC, where I often attend Vigil:

Photo of the Church Inside [stjohndc.org]

PS: Most of their services (including Vigils) are broadcast live on YouTube.

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And in this link you can find a photo of the Greek Catholic Cathedral in Uzhorod (no analoy / tetrapod)

https://www.byzcath.org/forums/ubbthreads.php/galleries/376854

In the Greek and Antiochian monastic tradition the festal icon is enthroned in the back entrance of the church at the conclusion of vespers when those the days when the Λιτή procession with verses are prescribed and not in the center of the church, although this is often the adaped custom in parishes - probably due to the absence of a significant exonarthex in most parish churches. Often a special analogia is placed at the entrance explicitly for the feast so that the monks or faithful may reverence the icon before entering the narthex of the church - usually at the same location as the kouvouklion at Pascha. For us the tetrapod is not used for the holding of icons but is only brought into the templet when specifially needed (memorial services to hold the koliva, for weddings, blessing of graps at Transfiguration etc.)