yes,it is possible to install apk file from personal website. Change the settings to support 3rd party installations.Practically when you try to install a 3rd party app, first MIUI is trying to install it from Mi market but if it's not connecting then it will install locally. That's why you need to cut off your Internet connection, in order to work. In case not working, try it again, maybe a few times. It could be due to the timing of you starting the download and turning off wifi and data not first enough.