A few weeks ago, I upgraded the touchpad of my X240 to the newer X250's variant featuring physical buttons. It worked out-of-the-box on Linux and using a specific driver version also under Windows 7.
After upgrading to Windows 10, the physical buttons wouldn't work at all and I started messing around with the Synaptics driver. It seems that the wrong driver is installed, as soft buttons are reported in the control panel.
When I poked through the SynPD.inf file, I noticed that there are quite a few registry settings that influence the behaviour of the driver. I researched my device ID and the device ID of the X250 and found out that the X250's device ID is LEN0046, while mine is LEN0038.
I came up with a registry patch file (it's actually a .inf, you need to install it with a right click → Install) that converts the settings to LEN0046. I only incorporated the changes necessary for LEN0038 → LEN0046, but I'm quite positive it works with other devices as well.
You can download the patch file here.