Penalties for excessive server usage due to backups

Hi everyone. My wife and I have been using i-MSCP for the past 4 or 5 years and we're very pleased with it. I'm having a "unique" problem with a vService provider. We've had either a root server (during the 90s) or a vServer for over 20 years, most recently with a provider whom we signed up with in 2014.

During the past 20+ years we've always had similar domain sizes and usage, consisting primarily of emails, photo albums, a few music files, and so on. Throughout this time there's always been one domain or another that was used for professional purposes, ranging in total file size from 1 GB to 3 GB for that entire domain. Little to no automation, videos, streaming media or other taxing items, mostly just raw data consisting of html, xml, jpg, png, and a few php scripts. In over 20 years we've never ever had any "excessive use" issues with any server/vServer provider ... UNTIL NOW ... even though the server hardware configurations have improved tremendously throughout all of this time.

Lately we've been receiving warnings for our vService provider that we'd be penalized or fined or that our vServer may even be shut down completely, if we didn't curb the excessive usage or drain that our vServer is generating on the vServer provider's system i.e. their other clients. This has never occurred before and little to nothing has changed on our domains during the past couple of years. As a matter of fact, we've even removed domains and lessened our email usage, yet suddenly our vServer is (supposedly) generating a serious problem ??? (see attached images)

We do have a trusted Admin that we hire on a job by job basis. We showed our admin the information and were told that based on our vServer stats it should be impossible to create such a massive drain on our vServer providers system, that it would impact their other clients. The admin went as far as to say that the claim was preposterous, followed by implying that perhaps the provider's equipment was faulty, slow, or outdated. However, since we paid for a "killer system" based on our personal minimal requirements, I'm now looking for a second opinion. I'm including the specs of the exact vServer which we're running, along with the providers screenshot of a log, where he claims there's proof that our vServer is bogging everything else down.
We're interested in what you think about the provided log image, compared to the hardware that we paid for.
Thank you for your time.

.xcessive_Turbo_400i4.pngxcessiveserver_usage.png

Thanks a lot for the advice and clarification. Definitely something to keep in mind from now on. I'm curious though, if you can verify or clarify that based on the log file .gif, our vserver is truly and clearly (as our provider claims) managing to severely impact the use of other clients just because of the backup that's taking place?

I'm really curious about this because we have very limited server knowledge. So my wife and I always figured that as long as we have a vServer with hardware configurations that "wildly surpass" anything that we might ever need, we'd be good to go? After all, what's the use of paying for "dedicated multiple cpu cores with oodles of ram and disk space" if all of those specs aren't enough to make sure that our vserver isn't negatively impacting someone else?

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Thank you so much for all of your help. We'll keep what you said in mind. I'll mention your suggestions to our admin as well since we want to make sure that we avoid further problems down the road. Have a great evening.