In general, I would look for information on such matters at the Irish state's organ responsible for collecting personal income tax, the Cain agus Custaim na hElreann - either on their website, or even go down to your local tax office and ask for a consultation. Many people don't realize this, but those tax clerks: 1. Know that tax code and 2. Tell you have to report things correctly, what you owe and what you don't. Now, sure, they will probably provide a strict interpretation of laws and regulations, but unless you're doing financially-complex business this shouldn't matter.
Specifically, it seems that you should not be paying any income tax in the Netherlands income tax at all - but rather pay your taxes in Ireland. You see, the Netherlands and Ireland have a(t least one) bilateral agreement on taxation. Either Article 13 or Article 14 should apply to you, and they say:
Article 13 Independent Personal Services
Income derived by a resident of one of the States in respect of professional services ...shall be taxable only in that State ...
The term "professional services" includes independent scientific, literary, artistic, educational or teaching activities as well as the
independent activities of physicians, lawyers, engineers, architects,
dentists and accountants.
Article 14 Dependent Personal Services
... salaries, wages and other similar remuneration
derived by a resident of one of the States in respect of an employment
shall be taxable only in that State unless the employment is exercised
in the other State. If the employment is so exercised, such
remuneration as is derived therefrom may be taxed in that other State.
So, indeed, @RemoGerlich 's speculation seems to be true. The fact that they asked for a BSN means their systems assume all employees live in the Netherlands, which explains why they would tax you by default.
I will emphasize that I am not a tax expert and my answer is based solely on common sense and reading that treaty.