Svenja,
This should be documented somewhere in RIO, but the way you can prevent computers from downloading FPGA VIs to the CompactRIO if using NI-RIO 2.1.2 or earlier, is by going in MAX to the controller>>Software>>NI-VISA tree item, selecting the VISA Options page, browsing to VISA Server>>Security and enabling/disabling access to computer as you see it fit.
If you are running into this problem because you trigger the compile of the FPGA VI through the VI's run arrow, I suggest you use the alternative way for compiling an FPGA VI which is to browse to it in the LabVIEW Project, right-click and select Compile. If you do this, the FPGA VI will not be automatically downloaded after is compiled.
(TIP) Something that I think not many people know about but it is very useful, is the "Target-Specific Properties" right-click option on FPGA VIs. This option gives you information about whether the VI needs to be recompiled and a bit more information such as when was the last time it was compiled and that compile results (like FPGA utilization). I believe this feature was added with LV FPGA 8.2.
Hope this helps.
JMota