Open Source license obligations are usually triggered on distribution of the software. That is, if you are only distributing your MIT-licensed NPM package via GitHub but none of its (transitive) dependencies, then it's not you who's creating a potentially conflicting license mix (due to maybe contradicting license obligations).
So you're fine as your NPM package only refers to the other packages via its package.json, but these are not included in your distribution. Instead, you require your users to run npm install.
Things would be different if you were distributing e.g. a ZIP archive which for some reason includes your package plus all dependencies. Then it would be you (re-)distributing all the packages, and you would be liable for any license compliance issues.
BTW, this is also why it usually makes a big difference whether you link a dependency dynamically or statically, but that concept does not really apply to JavaScript, and I'm mentioning it only for completeness.