Orders do not show up in customers account until processing state

It sounds like your incoming orders are assigned a state of pending_payment until the invoice is added. If you take a look at

/app/code/core/Mage/Sales/etc/config.xml

<config>
    <global>
        <sales>
            <order>
                <states>
                    <new translate="label">
                        <label>New</label>
                        <statuses>
                            <pending default="1"/>
                        </statuses>
                        <visible_on_front>1</visible_on_front>
                    </new>
                    <pending_payment translate="label">
                        <label>Pending Payment</label>
                        <statuses>
                            <pending_payment default="1"/>
                        </statuses>
                    </pending_payment>

you will notice this state does not have a <visible_on_front>1</visible_on_front> node

Your options here are to either use another state for the incoming orders or to allow this state to be shown. For the second option you can use the following:

<config>
    <global>
        <sales>
            <order>
                <states>
                    <pending_payment translate="label">
                        <visible_on_front>1</visible_on_front>
                    </pending_payment>
                </states>
            </order>
        </sales>
    </global>
</config>

in your own custom extension's etc/config.xml file.