Figure 1 shows the surface observations at 1:00 pm CDT, which shows an occluding low pressure across northern Manitoba with a trough of low pressure extending southwest across Saskatchewan. This trough was the focus for thunderstorms across central Manitoba in the morning hours of June 20th, which ultimately led to this tornado.

According to Environment and Climate Change Canada (2018), an F0 tornado touched down at 12:00 pm CDT near Cross Lake, MB. The track and width of the tornado was not documented by ECCC. The tornado caused no fatalities, injuries or property damage.
Sources
NWS Weather Prediction Center Surface Analysis Archive. (2017). Surface analysis 18Z Thu Jun 20 1996. Retrieved from: https://www.wpc.ncep.noaa.gov/archives/web_pages/sfc/sfc_archive.php
Environment and Climate Change Canada Data. (2018). Canadian National Tornado Database: Verified Events (1980-2009) – Public. Retrieved from: http://donnees.ec.gc.ca/data/weather/products/canadian-national-tornado-database-verified-events-1980-2009-public/