Tides coming in is normal, but there are rivers that change direction for other reasons. The Chicago River and the Mississippi can change direction due to storm surges, for example (for the Chicago River, that temporarily returns it to its flow direction, into Lake Michigan (https://en.wikipedia.org/wiki/Chicago_River#Course))
“As the monsoon rain begins, the water level of the river begins to rise. As the water level continues to rise, the flow of the river reverses. The water level of the Tonlé Sap increases by about 10 metres (33 ft), the flow of the Mekong gradually decreases at the end of the rainy season, and the flow of the Tonlé Sap then reverses and began to replenish the flow of the Mekong.”
A better example is https://en.wikipedia.org/wiki/Tonl%C3%A9_Sap#Geography:
“As the monsoon rain begins, the water level of the river begins to rise. As the water level continues to rise, the flow of the river reverses. The water level of the Tonlé Sap increases by about 10 metres (33 ft), the flow of the Mekong gradually decreases at the end of the rainy season, and the flow of the Tonlé Sap then reverses and began to replenish the flow of the Mekong.”