A user can switch between his allowed companies with the Preferences menu, but he will always see only the selected company with the current record rules.

If you want your user to see the records of all his allowed companies at the same time, you have to edit the ir.rule for this object and put something like that:

    <record id="product.product_comp_rule" model="ir.rule">
        <field name="domain_force">['|',('company_id','in',[c.id for c in user.company_ids]),('company_id','=',False)]</field>
    </record>