XSLT: can I limit the application of template and 'connect' it to some apply-template call?

To the best of my knowledge, XSL works as follows: it chooses some nodes to process via and then applies to each node in this selection.

I am confused because looks like here we have the same selection of SOMETHING twice: first in apply-template, and then in template match. Please consider my example below. I have got what I wanted: replaced the tags inside the Projects with PMatch tags only if the text attribute was not empty. But as you see, I have specified this condition twice! Is this a normal way?

XML

<?xml version="1.0" encoding="UTF-8"?>
<Manager text="this is a manager">
    <Name text="true name">Ivan</Name>
    <Projects text="ps">
        <Project text="ba">Bank</Project>
        <Project text="ca">Cars</Project>
        <Project>Business</Project>
    </Projects>
</Manager>

XSL

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="2.0" xmlns:foo="myFoo" xmlns:xsl="http://ift.tt/tCZ8VR" xmlns:fo="http://ift.tt/vyPH5E" xmlns:xs="http://ift.tt/tphNwY" xmlns:fn="http://ift.tt/pEXiIz">
    <xsl:output method="xml" encoding="UTF-8" indent="yes"/>
    <xsl:template match="/Manager">
        <ThisIsWhatIWantToSeeInName>
            <xsl:apply-templates/>
        </ThisIsWhatIWantToSeeInName>
    </xsl:template>
    <xsl:template match="Name">
        <NewName>Rihanna</NewName>
    </xsl:template>
    <xsl:template match="Projects">
        <Jobs>Jo-Jobs</Jobs>
        <NewJobs>
        <xsl:apply-templates select="Project[@text != '']"/>
        </NewJobs>
    </xsl:template>
    <xsl:template match="Project[@text != '']">
        <PMatch><xsl:value-of select="@text"/></PMatch>
    </xsl:template>
</xsl:stylesheet>

Result:

<?xml version="1.0" encoding="UTF-8"?>
<ThisIsWhatIWantToSeeInName xmlns:fn="http://ift.tt/pEXiIz" xmlns:fo="http://ift.tt/vyPH5E" xmlns:foo="myFoo" xmlns:xs="http://ift.tt/tphNwY">
    <NewName>Rihanna</NewName>
    <Jobs>Jo-Jobs</Jobs>
    <NewJobs>
        <PMatch>ba</PMatch>
        <PMatch>ca</PMatch>
    </NewJobs>
</ThisIsWhatIWantToSeeInName>

To escape from double selection specification I tried the following:

1) I tried to make apply-template selection wider by selecting all the Proejcts. But when the template finds only those which have text attributes - others a send to default templates which results in some plain text in my XML. Can I affect this behaviour somehow? Can I turn off default templates?

2) I tried to limit the apply-template selection as much as I can. OK, but if I make now template match wider like match='/' (because all the correct node are selected in apply-templates) - my template wil match many elements before this part of code, it will match even the root node. May be, I can 'connect' somehow my template to the place where it is applied? I want to be sure that my template is called only where I want.