Well that depends on what the previous owner has done to the jeep. On a normal factory functioning yj that shouldn't happen. When you turn either tire the opposite tire shouldn't turn. You "might" get the driveshaft to turn my spinning the driver side tire. HOWEVER!! If the previous owner has modified the front axle (as I have) that all sounds normal.
The reason behind all of this is in a factory setup there is a vacuum actuated motor that engages and disengages the front axle. The axle shaft going from the center differential to the passenger side is a 2 piece shaft with a shift collar that slides between the 2 to engage the front end. It is prone to failure because it requires engine vacuum to operate and that comes from some cheap hard plastic lines that get brittle with age and break. Because your 4WD is dependent on those lines, some of us have replaced those vacuum lines with a product called Posilock which replaces those vacuum lines by a hand operated cable that you mount on or under your dash. Others have rigged up the front axle to turn all the time like the newer TJ's are set up. You can replace the YJ 2 piece shaft with a TJ single piece shaft or do like I did and take the vacuum motor apart and install a heavy duty spring to keep it in the engaged position all the time. Which ever way it is/was done those vacuum lines are no longer required.
Hope this helps, and welcome to the forum or nut house as some of us call it.