In GPLV3, the following language appears to exempt contractors under reasonable conditions:
You may convey covered works to others
for the sole purpose of having them
make modifications exclusively for
you, or provide you with facilities
for running those works, provided that
you comply with the terms of this
License in conveying all material for
which you do not control copyright.
Those thus making or running the
covered works for you must do so
exclusively on your behalf, under your
direction and control, on terms that
prohibit them from making any copies
of your copyrighted material outside
their relationship with you
Even without the above language, you can meet the terms of this or older GPL versions by providing (or offering to provide) source code to those people who receive the binaries. You need to extend the terms of the GPL to them, but if "them" is you and your customer, nothing has changed, the SW was already GPLed and they were already a party to the agreement. You are under no obligation to provide your work to the general public and nothing seems to change as a result of your relationship to the customer except for rights granted to you that you need not exploit if you don't want to.
To answer your exact question: the code does not "become open sourced" except in the sense that once they deliver it (under V1 or V2) to you, then you specifically have the right to publish it as you like. If they trust you not to do that (and why not, it doesn't benefit you to rock the boat) then no "open source" event happens other than in a legalistic sense. That is, the party that receives the code gets full source rights, but no one is ever required to offer it to the general public.
From the day your customer got the SW they were already required to (offer to) provide source to those who received binaries. If they never distribute binaries their modifications can be proprietary, and even if they do distribute the obligation can be satisified between them and the receipients. Obviously, with enough distribution someone eventually really will publish it.
So, technically, there are rights granted by the GPL (with the above GPLv3 exception) on transfers between your two companies, but they are abstract and do not involve the general public unless you want them to.