Do exercises in a theoretical reference book need to be solved when doing research?
You are definitely looking at the wrong factor here. The question for you should not be "Should I solve the examples?", but rather "Do I understand the technique well enough to confidently apply it to my own research?".

If the answer to the second question is yes, you don't need to waste your time on doing more examples. If the answer is no, you need to study the technique more before applying it, and doing the examples may or may not be a good way to do it. However, in the second case, doing the examples cannot be "too time-consuming", as you will need to spend more time on learning the technique anyway. At the end of the day, it isn't about "solving as many examples as possible", but about understanding the material well enough. As a young researcher, you should be advanced enough to tell when this is the case.

That being said, the way how you phrased the question makes me wonder to what extend you actually understand the technique. Specifically:


  I started the reference book in the middle, while the exercises may require some previous chapters' techiniques, which I may not know and may not be directly related with my current research.


Of course one needs to know the concrete example to be sure, but if you are unable to do the examples because you have not read the previous text book sections, it seems to me that your understanding of the overall area is not all that great yet.