Material Design not styling alert dialogs

I've added the appCompat material design to my app and it seems that the alert dialogs are not using my primary, primaryDark, or accent colors.

Here is my base style:

<style name="MaterialNavyTheme" parent="@style/Theme.AppCompat.Light.DarkActionBar">
    <item name="colorPrimary">@color/apptheme_color</item>
    <item name="colorPrimaryDark">@color/apptheme_color_dark</item>
    <item name="colorAccent">@color/apptheme_color</item>
    <item name="android:textColorPrimary">@color/action_bar_gray</item>
</style>

Based on my understanding the dialogs button text should also use these colors. Am I wrong on my understanding or is there something more I need to do?

---

Solution:

The marked answer got me on the right track.

<style name="MaterialNavyTheme" parent="@style/Theme.AppCompat.Light.DarkActionBar">
    <item name="colorPrimary">@color/apptheme_color</item>
    <item name="colorPrimaryDark">@color/apptheme_color_dark</item>
    <item name="colorAccent">@color/apptheme_color</item>
    <item name="android:actionModeBackground">@color/apptheme_color_dark</item>
    <item name="android:textColorPrimary">@color/action_bar_gray</item>
    <item name="sdlDialogStyle">@style/DialogStyleLight</item>
    <item name="android:seekBarStyle">@style/SeekBarNavyTheme</item>
</style>

<style name="StyledDialog" parent="Theme.AppCompat.Light.Dialog">
    <item name="colorPrimary">@color/apptheme_color</item>
    <item name="colorPrimaryDark">@color/apptheme_color_dark</item>
    <item name="colorAccent">@color/apptheme_color</item>
</style>

UPDATED ON Aug 2019 WITH The Material components for android library:

With the new Material components for Android library you can use the new com.google.android.material.dialog.MaterialAlertDialogBuilder class, which extends from the existing androidx.appcompat.AlertDialog.Builder class and provides support for the latest Material Design specifications.

Just use something like this:

new MaterialAlertDialogBuilder(context)
            .setTitle("Dialog")
            .setMessage("Lorem ipsum dolor ....")
            .setPositiveButton("Ok", /* listener = */ null)
            .setNegativeButton("Cancel", /* listener = */ null)
            .show();

You can customize the colors extending the ThemeOverlay.MaterialComponents.MaterialAlertDialog style:

  <style name="CustomMaterialDialog" parent="@style/ThemeOverlay.MaterialComponents.MaterialAlertDialog">
     <!-- Background Color-->
     <item name="android:background">#006db3</item>
     <!-- Text Color for title and message -->
     <item name="colorOnSurface">@color/secondaryColor</item>
     <!-- Text Color for buttons -->
     <item name="colorPrimary">@color/white</item> 
     ....
  </style>  

To apply your custom style just use the constructor:

new MaterialAlertDialogBuilder(context, R.style.CustomMaterialDialog)

To customize the buttons, the title and the body text check this post for more details.

You can also change globally the style in your app theme:

 <!-- Base application theme. -->
 <style name="AppTheme" parent="Theme.MaterialComponents.Light">
    ...
    <item name="materialAlertDialogTheme">@style/CustomMaterialDialog</item>
 </style>

---

WITH SUPPORT LIBRARY and APPCOMPAT THEME:

With the new AppCompat v22.1 you can use the new android.support.v7.app.AlertDialog.

Just use a code like this:

import android.support.v7.app.AlertDialog

AlertDialog.Builder builder =
       new AlertDialog.Builder(this, R.style.AppCompatAlertDialogStyle);
builder.setTitle("Dialog");
builder.setMessage("Lorem ipsum dolor ....");
builder.setPositiveButton("OK", null);
builder.setNegativeButton("Cancel", null);
builder.show();

And use a style like this:

<style name="AppCompatAlertDialogStyle" parent="Theme.AppCompat.Light.Dialog.Alert">
        <item name="colorAccent">#FFCC00</item>
        <item name="android:textColorPrimary">#FFFFFF</item>
        <item name="android:background">#5fa3d0</item>
    </style>

Otherwise you can define in your current theme:

<style name="AppTheme" parent="Theme.AppCompat.Light">
    <!-- your style -->
    <item name="alertDialogTheme">@style/AppCompatAlertDialogStyle</item>
</style>

and then in your code:

 import android.support.v7.app.AlertDialog

    AlertDialog.Builder builder =
           new AlertDialog.Builder(this);

Here the AlertDialog on Kitkat: