You mean ISI WOS, I assume? Foremost, you should cite articles that truly are a base and reference for your own article. Citing ISI WOB articles is not necessary, but ISI WOS journals are of selected quality (not without biases though), so they usually are a good reference.
Sorry for that I mean ISI Web of science, but it comes to me that considering ISI journals, citation from ISI WOB sounds important i.e reviewers of course will also review the references that if not happy with references including finding missing in article, it will help them reject paper, I guess.
Usually, a journal expects you to cite some articles it has published before (not just to boost its impact factor, but also to show how you will advance the field/results of previous studies published there). Also, it makes sense to cite other journals as then you can demonstrate your knowledge of the field and also explain why you did something in this way (is this topic important, has somebody done it in this way before you or suggested studying this...).
Interesting question with so many questions and posts on RG about gaming the system. Apart from the mega science journals and now mega open access journals, the traditional role of the journal was to provide a forum for a community of scholars to publish research on a specific topic where they shared an interest. Those scholars would generally form the editorial board and the majority contributors and in the past might have shared a physical connection, same university/research centre/country/language/attend the same conferences.
The other way to look at it is for the journal to define the research agenda for a specific topic, with changes (globalisation) in publishing it is more likely that they will be an international community with a shared interest in a topic.
If ISI though its selection process (and there are some issues here) selects what is excellent then you can see a certain inevitability in citation patterns. Advice I gave to students beginning research, or part of it, was know your journals, the ones that define your research area and subscribe to the electronic tables of contents as a current awareness strategy.
I spent, and still do spend a lot of time collating and refining lists of key journals in areas that I have responsibility for as a librarian, to ensure my users have access to these titles. There is, for example, a core collection in Emergency Medicine, Advertising, Marketing, Economics and so on. You can see I have had a varied career. Most of the significant titles will be picked up by ISI WOS. So you will inevitably cite ISI WOS journals, but hopefully for the right reasons.
That`s fine, it is good suggestion to direct ourselves to specific journals by knowing our specialization (eg., personality -- Personality and Individual Differences), of course it will bring us to cite from our listed journals which is the Web of Science, as you said. Thanks Matt.
References must be cited as per need of the paper - whether from ISI web listed journal, IF journals or journals not having IF or a new journal. But citing references from ISI web listings help journals improve their IF respectively
I also learnt that citing various sources is always priority rather than popularity of sources. To some extent, its good to give a broad perspective to the manuscript.