I have that reading problem too, but I have learned that it only happens when I have qidian running on both at the same time.
For instance I have qidian library open in a browser on my laptop. Then I just close or leave my laptop without closing the browser(so everything is still open).Then I go on my phone and start reading, then I stop reading and come back to my laptop, the qidian library will not have the read chapters from my phone, and refresh is useless because it will just change the read chapters to what the laptop says and not my phone. This also happens in the reverse where I have qidian open on my phone and I start reading on the laptop.
I have no problems though if qidian is only open on one device and I close the application in that device before I start to use another. It's not very user friendly that's for sure....I feel like they need a manual sync button maybe to make it more cross device friendly.