Praise be to Allah.
The Mushaf al-Tajweed mentioned in the question is something into which great effort has been put, and like any other human action it is not free of mistakes or errors. Some specialists have pointed out these mistakes.
What we are talking about here is not the actual words of Allah which are written in the Mushaf; rather we are talking about the invention of a way to present them. No doubt the people who produced this have put a lot of time, effort and money into it, and the method they have invented is something that is protected in sharee’ah, which gives them the right to sell it, hire it out and prevent anyone from using it without their permission. This is one of the intangible rights concerning which fatwas have been issued by specialists in our times, ruling that this right is to be protected.
What we have mentioned here about the ban on transgressing against the rights of others without their permission is the basic ruling. But there may be some cases in which it is permissible for you to use the printed Mushaf without the permission of the publishers. That is in the case where the format in which you want to benefit from the Mushaf has not been produced by the producers of the Mushaf that you are asking about. The coloured tajweed Mushaf (Mushaf al-Tajweed al-Mulawwan) mentioned in the question is that which is printed on paper and gathered between two covers to be read from. If the publisher does not have software for that Mushaf which can be installed on mobile phones, then it seems that it is permissible for you to make software which will enable mobile phone owners to benefit from it, and that will not affect the producers of the Mushaf, because of the different ways in which they are used, especially if the software is free.
See also the answer to question number 95173.
And Allah knows best.