a csv file will have no coordinate system. If you used the Define projection tool to give it one, and got it wrong, then the points will be in the wrong location. It would be better to provide a sample of the coordinates to help decide what the problem is. Also, it is never a wise idea to bring in data into a dataframe unless the coordinate system is know first. Insert a new dataframe, then add the data to it, examine the coordinates and at least decide whether the data appear to be in decimal degrees or a projected coordinate system. You can proceed from there in deciding what the coordinate system and projection, if any, are.
Looks like one of the defined coordinate system is not correct.
What spatial reference are you using while converting the XY table to points? If the XY values are in Degrees (values ranging from -180 to +180), you should use an appropriate Geographic Coordinate System (e.g. GCS_WGS_1984).
If the points overlay correctly after applying the above coordinate system, you can reproject the point layer (if required) to the projection system of other layers.