Hello Amin,
In principle, AB apps doesn't have the "300ms of delay" problem, that is, we use the appropriate stuff to solve that in the past. Honestly, I don't think that we can do nothing about, except to note somethings, that maybe can enhance the GUI response. Let me to explain a bit.
If we follow the URL that you refer in your post (it's important to do it in avoiding any possible cache, since we can see what I want to explain mainly the first time we visit the URL) we can see a similar delay also in the browsers.
Maybe I am wrong, but, if you click or tap again in the menu items, that is, if you repeat the operation, the items changes faster, that is, more or less as expected. We can see this also in the browsers.
So my suggestion is to take a look at the app's code, and, look if they can be enhanced in some way, for example, if we can change the menu's items colors before the Report's data is trying to load or end to load.
My suggestion, in other words, is to try to change the menu's items before any other thing, seeing if this can do something useful: what we wanted is that the items' colors changes before we try to load the Report or anything else.
Note that do not have any problem to add other possible event or something like that: it's just that honestly I think that AB already does whatever is possible in order to get the best results. Maybe I am wrong and miss something... but this is what I can say right now...
P.D. About the usage of FastClick... I need to investigate it and see if certainly we can avoid their usage or what. However, it's rare that the library interfere in some way if they are not needed... the programmer maybe take this in consideration... but I want to investigate this anyway.