Confused Regarding Invitation Tracking

[edut]

I am using the Free version of Zoom. I created a Scheduled Meeting using the Desktop app (signed in with my work email, on my business domain) and included a client in the invitees list. I then went to the Zoom website to download the .ics file so I could send it to a client.  I opened the .ics file myself and added it to my personal calendar (Gmail account, via the MacOS Calendar app).

I sent the .ics file along with the joining details and a nice message to the client, using my work email (same as the email with which I created the meeting). The client accepted the invitation, but here is the weird part - I got an acceptance notification sent to my personal Gmail. I would have thought it would have gone to my work email. Now in my Gmail/MacOS calendar, I can see the client's acceptance status. How did my personal calendar get this status update? Also, is there an easier way to handle sending invites like this? Going to the website to get the .ics file is a pain.

I am worried that I somehow double-sent an invitation, which would look bad and also be confusing.

When inspecting the .ics file in a text editor, I see nothing in it containing any Gmail address. In fact, the only email address in the .ics file is my client's. How then could the client's acceptance be sent to my Gmail?