Which tenses do we use to talk about two consecutive* actions where* one happens* before another in the* present?
Which one sounds* more natural?
Since you are referring to "today," the word "now" may be used = "They didn't have problems until now." (simple past)
If you wish to use the word "today" = "They didn't have problems before today." (simple past)
No other verb needs to be used because a timeframe is given (ie. "now," "today"), meaning it is not necessary to create a subordinate clause. A simple, independent clause works just fine.
"They haven't had problems before, but now they are (having them)." (present perfect + present [or present progressive])
The words "having them" in parentheses, which is part of the present progressive ("are having") are not required and are usually left out; however, saying them is still correct. Since you are referring to the present (ie. "now," "today"), the present perfect must be used for the first event that occurred in the recent past, while the present should be used for the one that occurs after, in the present moment.