Pi-Hole does not control browser behavior, in particular pop-ups. Most browsers have options to not allow pop up windows, either globally or per site.
The spam will only be blocked by Pi-Hole if the domain that provides the spam is blocked by Pi-Hole. This would require the domain to be on one of your subscribed block lists, in your local blacklist or in a local regex filter.
These tools can help you determine how the content is served and then you can block as appropriate.
You should also verify that all the DNS traffic from the computer and iPhone are going to Pi-Hole, and that there is not another DNS server available to either of these clients. They should be using Pi-Hole only, or some of the DNS traffic will not be filtered.