I just bought this house. The toilet in the basement water jumps a d gurgles whenever the toilet upstairs is flushed. All fixtures, including the gurgling basement toilet flush/drain good. I also looked into the main cleanout into the main pipe leaving the house and the water is leaving fast and is not pooling up. This problem appears to have existed a long time because I can see the radiator by the basement toilet rusted from water splash.
Sounds like a problem in the venting. I don't grok drain venting well enough to know if it's the upstairs toilet or the downstairs one that's not properly vented (maybe both), but the rush of air getting pushed ahead of the flush needs to go somewhere, and that's what the vent stack is for. If the vent is clogged or nonexistant, the air will find the outlet it can (in this case, the downstairs toilet).