The free version of Pulse SMS may display banner ads. For an ads-free experience, you can consider upgrading to premium by going to Settings > Upgrade to Pulse SMS+.
On the other hand, if you're seeing other types of ads (i.e. not banner ads), it's possible that it's your phone's keyboard that displays them. That has nothing to do with Pulse SMS.
In addition, Pulse SMS generates previews for web links. It is possible that whatever link you are receiving would be for an ad, or that that ad would be the most prominent thing on the page and receive the preview. If you don't want these previews, you can turn them off from the Advanced Features menu by disabling the internal browser.