Hi,
Google suggest that you to include the hreflang tag also to the page itself:
If you have multiple language versions of a URL, each language page should identify different language versions, including itself. For example, if your site provides content in French, English, and Spanish, the Spanish version must include a rel=“alternate” hreflang=“x” link for itself in addition to links to the French and English versions. Similarly, the English and French versions must each include the same references to the French, English, and Spanish versions.