Do I need to check references of the paper with cross checking softwares?
Overall levels of plagiarism are completely irrelevant. What matters is whether there is at least one clear-cut case in which an extended phrase has been plagiarized from one of the sources. If so, the paper is unacceptable. In principle, one could have 1% similarity and clear plagiarism, or 20% similarity and no plagiarism. 

Once you look it in this light, it doesn't matter what the program does with respect to the references. Properly formatted references will look the same in any paper and so duplicating the text of any single reference is not considered plagiarism. (You can plagiarize references, however -- if I were to copy a set of important citations from another paper and then repeat them in order as if choosing them were my own work, this would be plagiarism.)

Of course, plagiarism checking software only catches the most obvious instances: direct plagiarism of blocks of text. One need not copy text exactly to have plagiarized. 

Finally, if any of the major publishers have "thresholds", they are being foolish.  As the software producers plainly admit, we are still at the point where a human needs to look at the instances reported by the program and make a judgement call about whether one is dealing with an actual instance of plagiarism. 

Edit: Given the comment below, it appears that some publishers are running submissions through a plagiarism detector upon submission. I suppose it might make sense to have a high cutoff above which everything gets rejected as probably plagiarized and not worth the editors' time -- but if they do that, "beating the plagiarism checker" is not what you need to be doing as a researcher. The last thing you want to do is submit a paper that slips in under the threshold yet contains instances of plagiarism that will come back to haunt you later.