Sounds like your modal is not clickable on a tablet!
If you show us what you did, perhaps we can tell you how to fix it.
Share a link to your page, or make a demo using jsFiddle or Plunkr.
Note that many mobile touchscreen OSs use double-tap to mean "zoom", and it is built-in to the browser. There are ways to disable it, but then the user will have an unexpected experience and may be confused, as they will expect double-tap to zoom and also would not anticipate that double-tap would do something else!
Maybe it is better to avoid double-click, and use some other interaction - perhaps a button that they can single-click? More and more users will have touchscreen devices and it's best to acknowledge that, and not use interactions that will create trouble for users of these devices. (Another example is "hover", which simply does not physically exist on a touchscreen. The mobile browsers try to fake it using the length of time that a spot has been touched, but it is a largely-unsatisfactory interaction.)
In any case, first show us what you did so that we do not have to guess.
