Participial phrase modifying...?

So first let me say that I am not looking for legal advice, and there's no legal dispute here regardless. This is just something that I came across and I've been thinking about, a mere curiosity, and there is a grammar question to be found below.

I signed up for a gym membership, and the contract reads in part: "An Annual Membership Fee will be billed to your account below on or around the 1st beginning on 06/01/2019 for $41.48 plus applicable taxes and will continue to be billed on or around the anniversary of that date each year thereafter until you cancel in accordance with this agreement."

I imagine that what they intend is for the first payment of $41.48 to come out on or around 06/01/2019, but if that's what they intend, then why not write: "...will be billed on or around 06/01/2019"? It's the "beginning on 06/01/2019" part that is throwing me for a loop. In other words, how can a payment be taken out "on or around" the 1st but also begin on the 1st?

So is "beginning on the 1st" a participial phrase, and, if so, then what is it modifying exactly? Is it modifying the noun phrase "the 1st," which it's closest to, or is it modifying "An Annual Membership Fee"? In short, what -- from a grammatical standpoint -- is this sentence really "saying" ?

Thanks in advance and, as always, you guys are the best!