The "dusty foot" bit related to those not resident in a market town who arrived in numbers, typically on foot, during the convening of the market. Where disputes arose over trade deals gone awry, or incidents of drunkenness or violence merited it, locals were empowered under law to set up a temporary tribunal with all the powers of what is now called a "district court" to quickly try such cases. Where these differed from magisterial or other crown courts in terms of procedure was that the accused didn't have to proffer a home address - it was deemed irrelevant - and also the verdict was determined by a panel of "judges", typically comprising the town's more eminent non-commercial notables, such as the schoolteacher, manor estate employees, the parson or vicar in post-reformation times, and similar. Innkeepers, monks and farmers were not preferred as judges, and where post-verdict appeals were made and succeeded it was very often on the grounds that the court contained one or more of these people whose neutrality might be questionable.
Verdicts and fines delivered by piepowder courts could be appealed, but only at the next "session", which would typically be the next time the market was held. This was an effective way of distinguishing between the true "piepowders" and those of more reputable standing who might have fallen foul of the previous court. The former were less likely to turn up and risk losing such an appeal, which normally meant a doubling of the original fine.
In towns or villages where the local dignitaries ran an effective magisterial court there was normally no need to appoint a piepowder court. True "dusty foots" were therefore wise to avoid such venues if they planned to get up to no good - these courts could impose larger fines without grounds for appeal, custodial sentences if required, and even death sentences.
So the short answer is that they were courts trying people who arrived with dusty feet, not necessarily those planning to do a runner. I'm not familiar with Spanish legal history, but any ad-hoc tribunal set up during market times or festivals etc, if they existed at all, would be the closest parallel.