You just need to use the standard valueUpdate
option of the value
binding where you can specify additional events to trigger your property change and with that the validation.
So you just need to add the valueUpdate: "blur"
setting on your bindings:
<label>First name:
<input data-bind='value: firstName, valueUpdate: "blur"' />
</label>
<br/>
<label>Last name:
<input data-bind='value: lastName, valueUpdate: "blur"' />
</label>
Demo JSFiddle.