VirtueMart calculates tax per shopper, and it can only apply a VAT rule once it knows where the shopper is. Two things decide what you see:

1. The tax rule (Products → Taxes & Calculation Rules): if it is limited to certain countries, a guest without an address gets no tax until checkout. For a single-country shop, leave the country empty or set it to your own country.
2. The shopper group (Shoppers → Shopper Groups → your default group): "Show prices with tax" applies to the cart too.

Also check Configuration → Pricing: the cart uses the same price display settings as the product page.

The rule is limited to Spain. Most of our guests are in Spain anyway – if I clear the country, do customers from outside the EU get VAT too?