Ah ah! that is because I tried for my own website ( building it at present) a similar effect ( and I have not yet totally mastered to achieve what I want!).
It seems there is one missing piece though : at present, your website still shows the small logo at start of loading the page.
You should add in the css :
homepage .header-title-logo, .homepage .header-mobile-logo a {
opacity: 0;
position: relative;
top: 0;
transition: all 0.3 s;
}
Then it should be as you wished it.