Asking good questions is always one way to ask. Though in this situation sounds like that wasn't an option.
Being able to identify the spots will be helpful in predicting the potential for wickback. (size of the spot can sometimes being and indication as well) Most hot liquids spilled have a large potential for wicking: Coffee, Tea, Urine, Gravy, blood ext. Also if a customer knows they had a large spill that they didn't get to quickly if at all.. also a red flag. Also be sure to find out how many times a customer has treated it and how they are treating it such as if they are pouring a spotter on and hoping for the best. (happens qute a alot).
If I find out from the customer that a spot has reappeared or that they can never get it to go away I try to go after the source and use a spot claw to extract.. atleast on a padded carpet that is. I'm almost always successful if I can identify a potential wickback situation and remove it via water claw. Typically I'll start with a hot water flush of the area.. (cold water for fresh blood), then water claw. open qd on solution like works well for flooding. I then follow with the spotter of choice.. tannin/acid side for urine coffee's, Tea's, and alkaline side for oily spills, sodas, gravy's. I dilute the spotter and flood the area and extract.. If i'm on the alkaline side i prefer to use an encap spotter or encap detergent as well for minimum residue. For Urine contamination, I'll use an odor urine specific product as my spotter to flood the area with dwell time such as osr. I finish with a clean water or fiber flood and extraction.. The process goes relatively quickly, but you need to charge extra for such service as well.
In the situation described where i'm walking unknowingly into the house. You have to prequalify with the customer that their is potential for wickbacks. And either charge enough up front that you can afford to follow up with a treatment or make it known that there will be a charge for a return visit.