Are you sure the camera is actually outputting 1080p25 over HDMI when set to record that internally? I'm not sure about the a6500, but there are lots of reports from Sony a7sii and a7rii users that the cameras only output 1080p50 or 1080p60 even when the internal recording mode is set to a different frame rate.
For example, see the following pages:
https://community.sony.com/t5/Alpha-SLT ... d-p/546322http://cheesycam.com/weird-60p-hdmi-out ... er-monitorAlso, keep in mind that the Roland V-1HD is not capable of outputting a 1080p25 signal. At 1080 resolution, the supported output formats are: 1080/59.94i, 1080/50i, 1080/59.94p, 1080/50p.
My suggestion would probably be to set the camera to capture at 1080p25 and the V-1HD switcher to output 1080i50. Usually what will happen in this case is that the each of the interlaced fields are actually from the same frame (captured at the same moment in time). The Mini Recorder should be able to accept the 1080i50 signal, and you can cleanly de-interlace the signal in OBS to turn it back into 1080p25 for streaming.