Did they also recommend this – https://www.siteground.com/tutorials/wordpress/limit-heartbeat/?

Make sure you have all the features enabled in WordFence that block spam bots.

Do you have any plugins, like, Broken Link Checker or EWWW Image Optimizer?

Ivan Atanasov from SiteGround here. Do you mind sharing your ticket ID so that I can revise it and investigate this issue for you?

The domain you included (ilmioloftcretaivo.com) appears to be available for purchase. I suspect you mistyped it.

You can also check if something is stressing on the server using AWStats in cPanel.

I confirmed that the limit was recently removed by one of our Customer Care representatives, so I went ahead and checked the history of your issue. Our team applied several modifications such as blocking the traffic from bad bots which helped with previous occurrences of this issue.

Turns our that this is not the first time you are exceeding your CPU seconds limit. And most of the times it was between 1:00AM and 7:00AM.

After checking the WordPress scheduled events I believe that the events in your WordPress are not well optimised, and there are a lot of events that coincide with each other. If this occurs often, you are likely to exceed the CPU limitation again, because the scheduled events take some time, and perform executions which exhaust the resources for your StartUp plan.

You might want to consider editing your scheduled events tables – meaning, you can spread the events through time with bigger intervals between them, and terminate the trivial events that are not vital for your website.

Additionally, you should consider disabling WordPress cron and setting up a Cron Jon from your cPanel. By doing this, you will be able to control the scheduled events even better and this should help you with the resource usage.

As for the visits you are referring to, note that you are using a StartUp plan. This hosting product will enable us to cache only the static content of your website. If you decide to upgrade to GrowBig the Dynamic caching will be available and it should lower the resource usage even further.

Of course, I would recommend testing with the scheduled events, and consider an upgrade if this is not enough for your website.

Feel free to post a Support Ticket if you need our assistance.

I believe that this will be a good place to start. The article will show you how to disable the WordPress Cron and replace it with a real Cron Job.

You can observe your website and determine at what time it is getting the most traffic, then schedule your Cron Job to execute at a time (times) when you observe the less traffic.

Please post a Support Ticket from your SiteGround User Area, if you need assistance with this.