JSFiddle - React, Tailwind, and code Playground

HTML

<img src="http://placehold.it/40x40">
<div class="loading-spinner-overlay-1">
  <div class="loading-spinner-background">
    <div class="loading-spinner-container">
      <img src="http://placehold.it/40x40">
    </div>
  </div>
</div>

<div class="loading-spinner-overlay-2">
  <div class="loading-spinner-background">
    <div class="loading-spinner-container">
      <img src="http://placehold.it/40x40">
      <p>
      Some very long long long text
      </p>
    </div>
  </div>
</div>

CSS

html {
    box-sizing: border-box;
}

*, *:before, *:after {
    box-sizing: inherit;
}

.loading-spinner-overlay-1 {
    background-color: aliceblue;
    left: 0;
    top: 60px;
    right: calc(100% - 300px);
    bottom: calc(100% - 300px);
    position: absolute;
    z-index: 9999;
    display: flex;
    align-items: center;
    justify-content: center;
}

.loading-spinner-overlay-2 {
    background-color: aliceblue;
    left: 0;
    top: 300px;
    right: calc(100% - 300px);
    bottom: calc(100% - 600px);
    position: absolute;
    z-index: 9999;
    display: flex;
    align-items: center;
    justify-content: center;
}

.loading-spinner-background {
    min-width: 100px;
    max-width: 50%;
    background-color: white;
    border-radius: 10px;
    display: flex;
    /* flex-direction: column;                  removed  */
    z-index: 1;
    padding: 20px;
}

.loading-spinner-container {
    min-height: 60px;                       /*  added/value changed (moved from *-background class)  */
    display: flex;
    flex-direction: column;
    flex-grow: 1;
    align-items: center;                     /*  added (changed)  */
    justify-content: center;                 /*  added  */
    width: 100%;
}

.loading-spinner-container > img {
    /* margin: auto;                             removed  */
}

.loading-spinner-container > p {
    text-align: center;
    margin: 0;
    width: 100%;
}