You need to check your vent pipe for a bird nest. Run a hose pipe (do not turn on the water) down the vent and if it is clear you need may need a larger or additional vent. A plumber will need to confirm.
If the toilet downstairs is rising as a result from flushing upstairs, The air vent could cause this as Ginger said but that would be dependent upon the location and piping system and typically a plugged, undersized vent causes water in toilets and sink traps to be sucked out when another appliance such as the upper level toilet or even tub is drained. If the drain line just past the lower level toilet is plugged just a bit and as the water runs down the pipe it becomes diverted and puts pressure by back flowing up the drain to the lower level toilet. The result would be exactly what your experiencing which can be rising water in bowl, gurgling sounds out of toilet and perhaps sink, or as you have splashes from large amounts of air being pushed out of pipe from water rushing down main stack line. If your not comfortable in using a power snake, I would have a professional pipe cleaning company come in and snake the main line from the roof down to the street. That should resolve your issue.