Please suggest how can I clarify my concern with the HR in a polite manner without sounding crude.
You engage in a conversation about the startup thethat goes something like "Tell me a little about the funding for this company..."
You explore the source of the startup's funding, if additional rounds of funding are planned, and what is the run rate at this time.
Your intent is to get a sense that the startup is well-funded, and well-run, and thus less likely to run into the kinds of problems you fear. (This is as opposed to asking "Will I be paid on time?" which could only elicit a less-than-useful answer of "Certainly.")
You may also choose to talk with one of your potential peers, where you can chat about how well the company is run, and probe a bit about finances and paychecks as well.
Ultimately though, it comes down to a matter of trust. Things can go south quickly in a small company, and you must trust that management will do the right thing. That's one of the risks of joining a startup that you must be willing to accept. Otherwise, a startup probably isn't for you.