Chilli and wasabi doesn't make you cry in the emotional sense. They stimulate the sinus and lacrimal glands to dilute and flush the irritant. There are other non-emotional triggers such as cutting onions. In that case we 'cry' to dilute and flush the sulphuric acid formed on the eye.
It's interesting to note that this isn't just a difference in cause. The actual chemistry of tears changes based on trigger, which means there's an objective difference between crying from the pain of a hot pepper and tearing up as a physical reaction to it. (And this shouldn't be totally surprising; any mammal tears up at eye irritants like onions or dust, so humans obviously have some additional mechanism controlling emotional tears.)
In fact, we apparently have (at least) four different types of tear! 'Basal' tears that keep our eyes wet have much higher lipid levels than any other type, and a higher fraction of their lipids are nonpolar. 'Reflex' and 'flush' tears are similar, they're both responses to irritants, but there seem to be differences between tears produced to remove solid/physical and liquid irritants. And then 'emotional' tears (which include pain) come with a host of hormones and other proteins basically absent from the general tear responses.
Chilli and wasabi doesn't make you cry in the emotional sense. They stimulate the sinus and lacrimal glands to dilute and flush the irritant. There are other non-emotional triggers such as cutting onions. In that case we 'cry' to dilute and flush the sulphuric acid formed on the eye.