MapPress doesn’t do any geocoding itself – it uses either Algolia Places or Google geocoders, based on which ‘engine’ you select in the settings.
Algolia is only accurate to the street level – not to individual street numbers. I think that’s why the marker is in the wrong place for 383 Woodbury Ave.
For the next version of MapPress I’ll add the MapBox and OSM geocoders, which seem to be more accurate than Algolia. I’ll also include a MapPress setting to allow you select which geocoder to use.
If you use the contact form to email me, I’ll send you a preview version to test as soon as it’s ready – later this week.
Until then, you could also switch to Google instead of Leaflet in the MapPress settings. Google has the best geocoder, but it requires an API key and has usage limits.