Is it normal for customer service agents to have access to your mobile number without you giving it to them?

I used the customer service online chat for help with a Photoshop issue earlier today and feel like my security has been compromised. I got put through to an agent who exited the chat within a minute of it starting. I then got a call from an American number (‭+1 (408) 606-3892‬) saying she was from Adobe and we had been cut off. Only thing is I never gave the chat agent my number? And when I google this number it comes up with a scam Adobe call? I started another chat immediately and got put through to someone else, and moments later as we were chatting got another call, this time from a London number (‭020 7365 5358‬). I’m based in the UK but again this number doesn’t come up with anything when I google it. This is extremely unusual for me to get two calls from two random (and different) unknown numbers, and when I asked the chat agent if he was calling me he said no, he didn’t have my number and that it was probably the previous chat person calling me. But if he didn’t have my number as I didn’t give it to him, how would the previous customer service agent have my number? 

Can someone please tell me if its normal for customer service agents to have your mobile number/be able to view your account details without you giving them permission to/giving them those details yourself?

I then gave access to this chat agent to my screen/laptop as I know/googled that this is a well known technique for fixing issues, although I did feel uneasy about it after the weird calls.

I then got an email from customercare-chatsupport@adobe.com with the below email. The email obviously appears fake due to the wording/format, but the email address seems legit? And the case number is the same as the one that appears on the Adobe website when I log in.

All in all a very strange experience, and concerned that my number has been accessed/passed onto random people? And especially given that I gave access to my laptop. Can someone enlighten on me if this is normal?